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IMAGINARY UNIT

  • Imaginary unit
  • Principal square root of minus 1

    real-number multiple of the imaginary unit is called an imaginary number. By combining the real numbers with the imaginary unit using addition and multiplication

    Imaginary unit

    Imaginary unit

    Imaginary_unit

  • Imaginary number
  • Square root of a non-positive real number

    An imaginary number is the product of a real number and the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number

    Imaginary number

    Imaginary_number

  • Complex number
  • Number with a real and an imaginary part

    extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i 2 = − 1 {\displaystyle i^{2}=-1} ; because

    Complex number

    Complex number

    Complex_number

  • Mathematical constant
  • Fixed number that has received a name

    .. (sequence A001113 in the OEIS). The imaginary unit or unit imaginary number, denoted as i, is a mathematical concept which extends

    Mathematical constant

    Mathematical_constant

  • Imaginary time
  • Concept in special relativity

    Mathematically, imaginary time is real time which has undergone a Wick rotation so that its coordinates are multiplied by the imaginary unit i. Imaginary time is

    Imaginary time

    Imaginary_time

  • Euler's formula
  • Complex exponential in terms of sine and cosine

    x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively

    Euler's formula

    Euler's formula

    Euler's_formula

  • Versor
  • Quaternion of norm 1 (unit quaternion)

    {\displaystyle \ \mathbf {r} \ } is an algebraic imaginary unit. There is a sphere of imaginary units in the quaternions. Note that the expression for

    Versor

    Versor

  • Euler's identity
  • Mathematical equation linking e, i and π

    number, the base of natural logarithms, i {\displaystyle i} is the imaginary unit, which by definition satisfies i 2 = − 1 {\displaystyle i^{2}=-1} ,

    Euler's identity

    Euler's identity

    Euler's_identity

  • Split-quaternion
  • Four-dimensional associative algebra over the reals

    In Hamilton quaternions there is a sphere of imaginary units, and any pair of antipodal imaginary units generates a complex plane with the real line.

    Split-quaternion

    Split-quaternion

  • Error function
  • Sigmoid shape special function

    {erfi} (z)=-i\operatorname {erf} (iz),} where i {\displaystyle i} is the imaginary unit. The name "error function" and its abbreviation erf {\displaystyle \operatorname

    Error function

    Error function

    Error_function

  • J
  • Tenth letter of the Latin alphabet

    the SI derived unit for energy. In some areas of physics, electrical engineering and related fields, j is the symbol for the imaginary unit (the square root

    J

    J

    J

  • J (disambiguation)
  • Topics referred to by the same term

    symbol used to denote the Bessel function j, used as the symbol for the imaginary unit ( − 1 {\displaystyle {\sqrt {-1}}} ) in fields where i is used for a

    J (disambiguation)

    J_(disambiguation)

  • Hyperbolic functions
  • Hyperbolic analogues of trigonometric functions

    Roger Cotes suggested to modify the trigonometric functions using the imaginary unit i = − 1 {\displaystyle i={\sqrt {-1}}} to obtain an oblate spheroid

    Hyperbolic functions

    Hyperbolic functions

    Hyperbolic_functions

  • Leonhard Euler
  • Swiss mathematician (1707–1783)

    value of a function, the letter i {\displaystyle i} to express the imaginary unit − 1 {\displaystyle {\sqrt {-1}}} , the Greek letter Σ {\displaystyle

    Leonhard Euler

    Leonhard Euler

    Leonhard_Euler

  • Riemann hypothesis
  • Conjecture on zeros of the zeta function

    t {\displaystyle t} is a real number and i {\displaystyle i} is the imaginary unit. The Riemann zeta function is defined for complex s {\displaystyle s}

    Riemann hypothesis

    Riemann hypothesis

    Riemann_hypothesis

  • Admittance
  • Ease of electrical current flow

    conductance (siemens); B is the susceptance (siemens); and j2 = −1, the imaginary unit. The dynamic effects of the material's susceptance relate to the universal

    Admittance

    Admittance

  • Number
  • Used to count, measure, and label

    The hypercomplex numbers include one real unit together with 2 n − 1 {\displaystyle 2^{n}-1} imaginary units, for which n is a non-negative integer. For

    Number

    Number

    Number

  • Complex plane
  • Geometric representation of the complex numbers

    and imaginary (y) parts: z = x + i y {\displaystyle z=x+iy} for example: z = 4 + 5i, where x and y are real numbers, and i is the imaginary unit. In this

    Complex plane

    Complex plane

    Complex_plane

  • Wick rotation
  • Mathematical trick using imaginary numbers to simplify certain formulas in physics

    mechanics formally akin to imaginary time in quantum mechanics: that is, it, where t is time and i is the imaginary unit (i2 = –1). More precisely, in

    Wick rotation

    Wick_rotation

  • De Moivre's formula
  • Theorem: (cos x + i sin x)^n = cos nx + i sin nx

    {\big (}\cos x+i\sin x{\big )}^{n}=\cos nx+i\sin nx,} where i is the imaginary unit (i2 = −1). The formula is named after Abraham de Moivre, although he

    De Moivre's formula

    De_Moivre's_formula

  • Momentum operator
  • Operator in quantum mechanics

    {\partial }{\partial x}}} where ħ is the reduced Planck constant, i the imaginary unit, x is the spatial coordinate, and a partial derivative (denoted by ∂

    Momentum operator

    Momentum_operator

  • Field (mathematics)
  • Algebraic structure with addition, multiplication, and division

    numbers C consist of expressions a + bi, with a, b real, where i is the imaginary unit, i.e., a (non-real) number satisfying i2 = −1. Addition and multiplication

    Field (mathematics)

    Field (mathematics)

    Field_(mathematics)

  • Group of rational points on the unit circle
  • Complex numbers with unit norm and both real and imaginary parts rational numbers

    on the unit circle there exists the rational point (a/c, b/c), which, in the complex plane, is just a/c + ib/c, where i is the imaginary unit. Conversely

    Group of rational points on the unit circle

    Group of rational points on the unit circle

    Group_of_rational_points_on_the_unit_circle

  • Jacobi–Anger expansion
  • Expansion of exponentials of trigonometric functions in the basis of their harmonics

    -th Bessel function of the first kind and i {\displaystyle i} is the imaginary unit, i 2 = − 1. {\textstyle i^{2}=-1.} Substituting θ {\textstyle \theta

    Jacobi–Anger expansion

    Jacobi–Anger_expansion

  • Cis (mathematics)
  • Function equal to cos x + i sin x

    cis x = cos x + i sin x, where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number

    Cis (mathematics)

    Cis_(mathematics)

  • Hermitian matrix
  • Matrix equal to its conjugate-transpose

    In the following example, i {\displaystyle \mathbf {i} } denotes the imaginary unit ( i = − 1 ) : {\displaystyle \left(\mathbf {i} ={\sqrt {-1}}\right)\

    Hermitian matrix

    Hermitian_matrix

  • Gelfond's constant
  • Constant e raised to the power of pi

    {\displaystyle e^{\pi }=(e^{i\pi })^{-i}=(-1)^{-i},} where i is the imaginary unit. Since −i is algebraic but not rational, eπ is transcendental. The numbers

    Gelfond's constant

    Gelfond's_constant

  • Bloch's theorem
  • Fundamental theorem in condensed matter physics

    {\displaystyle e} is Euler's number, and i {\displaystyle i} is the imaginary unit. Functions of this form are known as Bloch functions or Bloch states

    Bloch's theorem

    Bloch's theorem

    Bloch's_theorem

  • Fresnel equations
  • Equations of light transmission and reflection

    form where Ek is the (constant) complex amplitude vector, i is the imaginary unit, k is the wave vector (whose magnitude k is the angular wavenumber)

    Fresnel equations

    Fresnel equations

    Fresnel_equations

  • Conjugate (square roots)
  • Change of the sign of a square root

    where the square root is i = − 1 , {\displaystyle i={\sqrt {-1}},} the imaginary unit. As ( a + b d ) ( a − b d ) = a 2 − b 2 d {\displaystyle (a+b{\sqrt

    Conjugate (square roots)

    Conjugate_(square_roots)

  • List of common physics notations
  • System of Units ISO 31 Elert, Glenn. "Special Symbols". The Physics Hypertextbook. Retrieved 4 August 2021. NIST (16 August 2023). "SI Units". www.nist

    List of common physics notations

    List_of_common_physics_notations

  • List of types of numbers
  • numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit i {\displaystyle i} , where i

    List of types of numbers

    List_of_types_of_numbers

  • I (disambiguation)
  • Topics referred to by the same term

    Roman numeral for 1 i, imaginary unit, for which i2 = −1 I or In, identity matrix of indeterminate size (or of size n) I, unit interval, which contains

    I (disambiguation)

    I_(disambiguation)

  • Plane-wave expansion
  • Expressing a plane wave as a combination of spherical waves

    }({\hat {\mathbf {k} }}\cdot {\hat {\mathbf {r} }}),} where i is the imaginary unit, k is a real or complex wave vector of length k, r is a position vector

    Plane-wave expansion

    Plane-wave_expansion

  • −2
  • Negative integer two units from the origin in mathematics

    {\displaystyle 1+i} is a Gaussian prime and i {\displaystyle i} is the imaginary unit. The first few powers of negative two are −2, 4, −8, 16, −32, 64, −128

    −2

    −2

  • Electrical susceptance
  • Imaginary part of electrical admittance

    impedance (Z = R + jX), where the imaginary part is reactance (X) and the real part is resistance (R). In SI units, susceptance is measured in siemens

    Electrical susceptance

    Electrical_susceptance

  • Unit vector
  • Vector of length one

    vector part v is a unit vector in R 3 {\displaystyle \mathbb {R} ^{3}} . Thus the right versors extend the notion of imaginary units found in the complex

    Unit vector

    Unit_vector

  • Bicomplex number
  • Commutative, associative algebra of two complex dimensions

    numbers feature two distinct imaginary units. Multiplication being associative and commutative, the product of these imaginary units must have positive one

    Bicomplex number

    Bicomplex_number

  • Ordered field
  • Algebraic object with an ordered structure

    that the complex numbers cannot be ordered since the square of the imaginary unit i is −1 (which is negative in any ordered field). Finite fields cannot

    Ordered field

    Ordered_field

  • Nth root
  • Arithmetic operation, inverse of nth power

    has two imaginary square roots, ⁠ + i x {\displaystyle +i{\sqrt {x}}} ⁠ and ⁠ − i x {\displaystyle -i{\sqrt {x}}} ⁠, where i is the imaginary unit. In general

    Nth root

    Nth root

    Nth_root

  • Electrical impedance
  • Opposition of a circuit to a current when a voltage is applied

    the letter i {\displaystyle i} is used for electric current, so the imaginary unit is instead represented by the letter j {\displaystyle j} . In Cartesian

    Electrical impedance

    Electrical impedance

    Electrical_impedance

  • Quotient ring
  • Reduction of a ring by one of its ideals

    ⁠, with the class [ X ] {\displaystyle [X]} playing the role of the imaginary unit ⁠ i {\displaystyle i} ⁠. The reason is that we "forced" ⁠ X 2 + 1 =

    Quotient ring

    Quotient_ring

  • Cyclotomic polynomial
  • Irreducible polynomial whose roots are nth roots of unity

    and coprime to n {\displaystyle n} (where i {\displaystyle i} is the imaginary unit). In other words, the n {\displaystyle n} -th cyclotomic polynomial

    Cyclotomic polynomial

    Cyclotomic_polynomial

  • Phase factor
  • Type of complex number

    complex exponential, eiθ, where the variable θ is the phase and i is the imaginary unit. If a quantity like a scalar, vector, or a matrix (representing a wave

    Phase factor

    Phase_factor

  • Sign convention
  • Agreed-upon meaning of a physical quantity being positive or negative

    term "sign convention" is used more broadly to include factors of the imaginary unit i and 2π, rather than just choices of sign. In relativity, the metric

    Sign convention

    Sign_convention

  • Geometric series
  • Sum of an (infinite) geometric progression

    example can be found in Grandi's series. When the common ratio is the imaginary unit r = i {\displaystyle r=i} and a = 1 {\displaystyle a=1} , the partial

    Geometric series

    Geometric_series

  • Frustum
  • Portion of a solid that lies between two parallel planes cutting the solid

    Alexandria is noted for deriving this formula, and with it, encountering the imaginary unit: the square root of negative one. In particular: The volume of a circular

    Frustum

    Frustum

    Frustum

  • Unitary matrix
  • Complex matrix whose conjugate transpose equals its inverse

    written as U = eiH, where e indicates the matrix exponential, i is the imaginary unit, and H is a Hermitian matrix. For any nonnegative integer n, the set

    Unitary matrix

    Unitary_matrix

  • Blackboard bold
  • Typeface style used in mathematics

    Springer. "7. Standard number sets and intervals". ISO 80000-2 Quantities and Units: Mathematics (2nd ed.). International Organization for Standardization.

    Blackboard bold

    Blackboard bold

    Blackboard_bold

  • AC power
  • Power in alternating current systems

    it is represented as the imaginary axis of the vector diagram. Active power does do work, so it is the real axis. The unit for power is the watt (symbol:

    AC power

    AC power

    AC_power

  • Mass
  • Amount of matter present in an object

    part being their mass in the usual sense, and the imaginary part being the decay rate in natural units. However, in quantum field theory, a particle (a

    Mass

    Mass

    Mass

  • Math symbol i
  • Topics referred to by the same term

    The symbol i in mathematical equations may refer to: Imaginary unit (i), for which i2 = -1 Imaginary number Complex number i, an index variable in a matrix

    Math symbol i

    Math_symbol_i

  • Canonical commutation relation
  • Relation satisfied by conjugate variables in quantum mechanics

    x and px , i is the imaginary unit, and ℏ is the reduced Planck constant (h/2π), and I {\displaystyle \mathbb {I} } is the unit operator. In finite dimensions

    Canonical commutation relation

    Canonical_commutation_relation

  • Closed system
  • Type of system

    t}}\Psi (\mathbf {r} ,t)={\hat {H}}\Psi (\mathbf {r} ,t)} where i is the imaginary unit, ħ is the Planck constant divided by 2π, the symbol ⁠∂/∂t⁠ indicates

    Closed system

    Closed_system

  • Complex beam parameter
  • Specifies the properties of a Gaussian beam

    waist, at which q is calculated, zR is the Rayleigh range, and i is the imaginary unit. The complex beam parameter is usually used in ray transfer matrix analysis

    Complex beam parameter

    Complex_beam_parameter

  • Physical quantity
  • Measurable property of a material or system

    numbers, such as 1 or √2, e, the base of natural logarithms, i, the imaginary unit, π for the ratio of a circle's circumference to its diameter, 3.14159265

    Physical quantity

    Physical quantity

    Physical_quantity

  • Parseval's theorem
  • Theorem in mathematics

    {B(x)}}\,\mathrm {d} x,}    (Eq.1) where i {\displaystyle i} is the imaginary unit and horizontal bars indicate complex conjugation. Substituting A ( x

    Parseval's theorem

    Parseval's_theorem

  • Voltage divider
  • Linear circuit that produces an output voltage that is a fraction of its input voltage

    reactance of the capacitor, C is the capacitance of the capacitor, j is the imaginary unit, and ω (omega) is the radian frequency of the input voltage. This divider

    Voltage divider

    Voltage_divider

  • Ambiguity function
  • Function of propagation delay and Doppler frequency

    ^{*}} denotes the complex conjugate and i {\displaystyle i} is the imaginary unit. Note that for zero Doppler shift ( f = 0 {\displaystyle f=0} ), this

    Ambiguity function

    Ambiguity_function

  • Glossary of linear algebra
  • linear algebra over the real numbers with basis {1, i }, where i is an imaginary unit coordinate vector The tuple of the coordinates of a vector on a basis

    Glossary of linear algebra

    Glossary_of_linear_algebra

  • Total internal reflection
  • Complete reflection of a wave

    form where Ek is the (constant) complex amplitude vector, i is the imaginary unit, k is the wave vector (whose magnitude k is the angular wavenumber)

    Total internal reflection

    Total internal reflection

    Total_internal_reflection

  • Quaternion
  • Four-dimensional number system

    quaternions z = b i + c j + d k such that b2 + c2 + d2 = 1. Thus these imaginary units form a unit sphere in the three-dimensional space of quaternion vectors.

    Quaternion

    Quaternion

    Quaternion

  • Square root
  • Number whose square is a given number

    electricity where i traditionally represents electric current) and called the imaginary unit, which is defined such that i2 = −1. Using this notation, we can think

    Square root

    Square root

    Square_root

  • Capacitor
  • Electronic component

    fC}}\end{aligned}}} where ⁠ j = − 1 {\displaystyle j={\sqrt {-1}}} ⁠ is the imaginary unit and ⁠ ω {\displaystyle \omega } ⁠ is the angular frequency of the sinusoidal

    Capacitor

    Capacitor

    Capacitor

  • Gerchberg–Saxton algorithm
  • Algorithm for phase retrieval

    – forward Fourier transform IFT – inverse Fourier transform i – the imaginary unit, √−1 (square root of −1) exp – exponential function (exp(x) = ex) Target

    Gerchberg–Saxton algorithm

    Gerchberg–Saxton algorithm

    Gerchberg–Saxton_algorithm

  • Trigonometry
  • Area of geometry, about angles and lengths

    analytical identities for sine, cosine, and tangent in terms of e and the imaginary unit i: sin ⁡ x = e i x − e − i x 2 i , cos ⁡ x = e i x + e − i x 2 , tan

    Trigonometry

    Trigonometry

    Trigonometry

  • -i
  • Topics referred to by the same term

    demonymic suffix in English A pronominal suffix in Hebrew The negative imaginary unit (−i), a square root of -1 This disambiguation page lists articles associated

    -i

    -i

  • Electrical reactance
  • Opposition to current by inductance or capacitance

    formulas. j {\displaystyle \mathbf {j} } is used so as not to confuse the imaginary unit with current, commonly represented by ⁠ i {\displaystyle \mathbf {i}

    Electrical reactance

    Electrical_reactance

  • Quadratic equation
  • Polynomial equation of degree two

    are complex conjugates of each other. In these expressions i is the imaginary unit. Thus the roots are distinct if and only if the discriminant is non-zero

    Quadratic equation

    Quadratic_equation

  • Cartesian coordinate system
  • Coordinate system using perpendicular axes

    z = x + iy. Here, i is the imaginary unit and is identified with the point with coordinates (0, 1), so it is not the unit vector in the direction of the

    Cartesian coordinate system

    Cartesian coordinate system

    Cartesian_coordinate_system

  • Iota
  • Ninth letter in the Greek alphabet

    gives 1 2 3 4. The lowercase iota symbol is sometimes used to write the imaginary unit, but more often Roman i or j is used. In mathematics, the inclusion

    Iota

    Iota

  • Three Imaginary Boys
  • 1979 studio album by the Cure

    Three Imaginary Boys is the debut studio album by the English rock band the Cure, released on 8 May 1979 by Fiction Records, and reached number 44 on

    Three Imaginary Boys

    Three_Imaginary_Boys

  • Non-Euclidean geometry
  • Two geometries based on axioms closely related to those specifying Euclidean geometry

    –1, 0, 1 }. The Euclidean plane corresponds to the case ε2 = −1, an imaginary unit. Since the modulus of z is given by z z ∗ = ( x + y ϵ ) ( x − y ϵ )

    Non-Euclidean geometry

    Non-Euclidean_geometry

  • Grand Riemann hypothesis
  • {\displaystyle t} a real number variable and i {\displaystyle i} the imaginary unit. The modified grand Riemann hypothesis is the assertion that the nontrivial

    Grand Riemann hypothesis

    Grand_Riemann_hypothesis

  • Warburg element
  • Electrical impedance which models diffusion in dieletric spectroscopy

    where AW is the Warburg coefficient (or Warburg constant); j is the imaginary unit; ω is the angular frequency. This equation assumes semi-infinite linear

    Warburg element

    Warburg_element

  • Sallen–Key topology
  • Electronic filter topology

    {\displaystyle s=j\omega =2\pi jf} (here j {\displaystyle j} denotes the imaginary unit) is the complex angular frequency, and f {\displaystyle f} is the frequency

    Sallen–Key topology

    Sallen–Key_topology

  • Prony's method
  • Method to estimate the components of a signal

    the amplitude components of the series, j {\displaystyle j} is the imaginary unit ( j 2 = − 1 {\displaystyle j^{2}=-1} ). Prony's method is essentially

    Prony's method

    Prony's method

    Prony's_method

  • Residue theorem
  • Concept of complex analysis

    centered at 0 from a to −a. Take a to be greater than 1, so that the imaginary unit i is enclosed within the curve. Now consider the contour integral ∫

    Residue theorem

    Residue theorem

    Residue_theorem

  • Quaternionic representation
  • Representation of a group or algebra in terms of an algebra with quaternionic structure

    which satisfies j 2 = − 1. {\displaystyle j^{2}=-1.} Together with the imaginary unit i and the antilinear map k := ij, j equips V with the structure of a

    Quaternionic representation

    Quaternionic_representation

  • Mathematical notation
  • System of symbolic representation

    (constants). He introduced also the notation i and the term imaginary for the imaginary unit. The 18th and 19th centuries saw the standardization of mathematical

    Mathematical notation

    Mathematical notation

    Mathematical_notation

  • Pi
  • Number, approximately 3.14

    {\displaystyle z=r\cdot (\cos \varphi +i\sin \varphi ),} where i is the imaginary unit satisfying i 2 = − 1 {\displaystyle i^{2}=-1} . The frequent appearance

    Pi

    Pi

  • Breather
  • Type of nonlinear wave in physics

    with u a complex field as a function of x and t. Further i denotes the imaginary unit. One of the breather solutions (Kuznetsov-Ma breather) is u = ( 2 b

    Breather

    Breather

    Breather

  • Square (algebra)
  • Product of a number by itself

    expand the real number system to the complex numbers, by postulating the imaginary unit i, which is one of the square roots of −1. The property "every non-negative

    Square (algebra)

    Square (algebra)

    Square_(algebra)

  • Wiener–Khinchin theorem
  • Theorem relating stationary processes' autocorrelations and power spectra

    is the angular frequency, i {\displaystyle i} is used to denote the imaginary unit (in engineering, sometimes the letter j {\displaystyle j} is used instead)

    Wiener–Khinchin theorem

    Wiener–Khinchin_theorem

  • Summation
  • Addition of several numbers or other values

    ISBN 978-0201558029. In contexts where there is no possibility of confusion with the imaginary unit i {\displaystyle i} Although the name of the dummy variable does not

    Summation

    Summation

  • Baseband
  • Range of frequencies occupied by an unmodulated signal

    {\displaystyle Q(t)} the quadrature phase signal, and j {\displaystyle j} the imaginary unit. This signal is sometimes called IQ data. In a digital modulation method

    Baseband

    Baseband

    Baseband

  • Strehl ratio
  • Proportion of observed intensity to ideal intensity, in astronomical imaging

    |^{2}=|\langle e^{i2\pi \delta /\lambda }\rangle |^{2}} where i is the imaginary unit, ϕ = 2 π δ / λ {\displaystyle \phi =2\pi \delta /\lambda } is the phase

    Strehl ratio

    Strehl_ratio

  • Dirac algebra
  • Clifford algebra in 4 dimensions

    usually enlightening) to identify the presence of an imaginary unit in a physical equation. Such units arise from one of the many quantities in a real Clifford

    Dirac algebra

    Dirac_algebra

  • Pole–zero plot
  • Diagram showing the singularities of a given control system's transfer function

    {\displaystyle z=\pm {\frac {j}{2}}} , where j {\displaystyle j} is the imaginary unit. The pole–zero plot would be: Root locus Laplace transform Z-transform

    Pole–zero plot

    Pole–zero plot

    Pole–zero_plot

  • Wave impedance
  • Constant related to electromagnetic wave propagation in a medium

    through (corresponding to the imaginary component of the permittivity multiplied by omega). In the equation, j is the imaginary unit, and ω is the angular frequency

    Wave impedance

    Wave_impedance

  • Number theory
  • Branch of pure mathematics

    {\displaystyle 0} . The complex numbers extend the real numbers with the imaginary unit i {\displaystyle i} defined as the solution to i 2 = − 1 {\displaystyle

    Number theory

    Number theory

    Number_theory

  • Normal distribution
  • Probability distribution

    t}e^{-{\frac {1}{2}}\sigma ^{2}t^{2}}\,,} where ⁠ i {\displaystyle i} ⁠ is the imaginary unit. If the mean μ = 0 {\textstyle \mu =0} , the first factor is 1, and

    Normal distribution

    Normal distribution

    Normal_distribution

  • Dynamic modulus
  • Ratio used in material engineering

    ″ {\displaystyle G^{*}=G'+iG''\,} where i {\displaystyle i} is the imaginary unit. The ratio of the loss modulus to storage modulus in a viscoelastic

    Dynamic modulus

    Dynamic_modulus

  • Karatsuba algorithm
  • Algorithm for integer multiplication

    generalization of a similar complex multiplication algorithm, where the imaginary unit i is replaced by a power of the base. Let x {\displaystyle x} and y

    Karatsuba algorithm

    Karatsuba algorithm

    Karatsuba_algorithm

  • Sommerfeld radiation condition
  • Radiation boundary condition

    {\displaystyle {\hat {x}}={\frac {x}{|x|}}} (above, i {\displaystyle i} is the imaginary unit and | ⋅ | {\displaystyle |\cdot |} is the Euclidean norm). Here, it

    Sommerfeld radiation condition

    Sommerfeld_radiation_condition

  • List of numbers
  • {\displaystyle \mathbb {H} } , Unicode U+210D ℍ DOUBLE-STRUCK CAPITAL H). Imaginary unit: i = − 1 {\textstyle i={\sqrt {-1}}} nth roots of unity: ξ n k = cos

    List of numbers

    List_of_numbers

  • Linear combination
  • Sum of terms, each multiplied with a scalar

    is the base of the natural logarithm, about 2.71828..., and i is the imaginary unit, a square root of −1.) Some linear combinations of f and g are: cos

    Linear combination

    Linear combination

    Linear_combination

  • Permittivity
  • Measure of the electric polarizability of a dielectric material

    amplitudes of the displacement and electric fields, respectively, i is the imaginary unit, i2 = − 1 . The response of a medium to static electric fields is described

    Permittivity

    Permittivity

    Permittivity

  • Fourier transform
  • Mathematical transform that expresses a function of time as a function of frequency

    letter j is typically used for the imaginary unit instead of i because i is used for current. When using dimensionless units, the constant factors might not

    Fourier transform

    Fourier transform

    Fourier_transform

  • Unit circle
  • Circle with radius of one

    called the unit complex numbers. This is the set of complex numbers z such that | z | = 1. {\displaystyle |z|=1.} When broken into real and imaginary components

    Unit circle

    Unit circle

    Unit_circle

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IMAGINARY UNIT

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IMAGINARY UNIT

  • UNITY
  • Female

    English

    UNITY

    English name derived from the vocabulary word, UNITY means "oneness, unity."

    UNITY

  • Furlong
  • Surname or Lastname

    English and Irish

    Furlong

    English and Irish : apparently a topographic name from Middle English furlong ‘length of a field’ (from Old English furh ‘furrow’ + lang ‘long’), the technical term for the block of strips owned by several different persons which formed the unit of cultivation in the medieval open-field system of farming, or a habitational name from a minor place named with this word, such as Furlong in Devon or Shropshire. The surname is now chiefly common in Ireland, where a family of this name settled at the end of the 13th century.Possibly an Americanized form of French Ferland.

    Furlong

  • Humera
  • Girl/Female

    Arabic, Muslim

    Humera

    The Imaginary Bird who Soars the Highest

    Humera

  • Ayham |
  • Boy/Male

    Muslim

    Ayham |

    Imaginary

    Ayham |

  • Huma
  • Girl/Female

    Muslim/Islamic

    Huma

    An Imaginary bird

    Huma

  • Huma
  • Girl/Female

    Afghan, Arabic, Assamese, Gujarati, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi

    Huma

    Bird of Paradise; Daughter of King Bahman and Mother of Darab; Gold; An Imaginary Bird

    Huma

  • Tasavur
  • Girl/Female

    Indian

    Tasavur

    Imaginary picture

    Tasavur

  • Humera
  • Girl/Female

    Muslim/Islamic

    Humera

    The imaginary bird who soars the highest

    Humera

  • Tasavur
  • Girl/Female

    Muslim/Islamic

    Tasavur

    Imaginary picture

    Tasavur

  • Joynt
  • Surname or Lastname

    English

    Joynt

    English : presumably from Old French joint ‘united’, ‘joined’. The application as a surname is unclear.

    Joynt

  • Gascoigne
  • Surname or Lastname

    English

    Gascoigne

    English : from Old French Gascogne ‘Gascony’, hence a regional name. The name of the region derives from that of the Basques, who are found close by and formerly extended into this region as well; they are first named in Roman sources as Vascōnes, but the original meaning of the name, derived from a root eusk- in the non-Indo-European language that they still speak today, is completely obscure. By the Middle Ages the Basques had been displaced from most of Gascony by speakers of Gascon (a dialect of Occitan, related to French), who were proverbial for their boastfulness. In the 11th century Gascony united with Aquitaine and was thus held by England between 1154 and 1453. See Gascon.

    Gascoigne

  • Dicker
  • Surname or Lastname

    English (southwest)

    Dicker

    English (southwest) : occupational name for a digger of ditches or a builder of dikes, or a topographic name for someone who lived by a ditch or dike, from an agent derivative of Middle English diche, dike (see Dyke).English : regional name from an area of East Sussex, near Hellingly, called ‘the Dicker’ (hence also the hamlets of Upper and Lower Dicker), from Middle English dyker unit of ten (Latin decuria, from decem ‘ten’); the reason for the place being so named is not clear. It has been suggested that the reference is to a bundle of iron rods, in which sense dicras appears in Domesday Book. Such a bundle could have been the rent for property in this iron-working area. Surname forms such as atte dicker occur in the surrounding region in the 13th and 14th centuries.German and Jewish (Ashkenazic) : variant of Dick 2, from an inflected form.North German : variant of Low German Dieker, a topographic or an occupational name for someone who lived or worked at a dike (see Dieck).Americanized spelling of French Decaire.

    Dicker

  • Litwin
  • Surname or Lastname

    Polish, German, and Jewish (eastern Ashkenazic)

    Litwin

    Polish, German, and Jewish (eastern Ashkenazic) : from Polish litwin, an ethnic name for someone from Lithuania (Polish Litwa, Lithuanian Lietuva, a word of uncertain etymology, perhaps a derivative of the river name Leità). In the 14th century Lithuania was an independent grand duchy which extended from the Baltic to the shores of the Black Sea. It was united with Poland in 1569, and was absorbed into the Russian empire in 1795. The region referred to as Lite in Ashkenazic culture encompassed not only Lithuania but also Latvia, Estonia, Belarus, parts of northern Ukraine, and parts of northeastern Poland.English : from an Old English personal name, Lēohtwine, composed of the elements lēoht ‘light’, ‘bright’ + wine ‘friend’.

    Litwin

  • Cockayne
  • Surname or Lastname

    English

    Cockayne

    English : nickname for an idle dreamer, from Middle English cokayne ‘cloud-cuckooland’, name of an imaginary paradise (Old French (pays de) cocaigne, from Middle Low German kōkenje, a diminutive of kōke ‘cake’, since in this land the houses were supposed to be made of cake).Americanized spelling of French Cocagne, from an Occitan word meaning ‘profit’, ‘advantage’, used as a personal name from the Middle Ages.

    Cockayne

  • Gay
  • Surname or Lastname

    English and French

    Gay

    English and French : nickname for a lighthearted or cheerful person, from Middle English, Old French gai. In Middle English the term could also mean ‘wanton’, ‘lascivious’ and this sense may lie behind the surname in some instances.English (of Norman origin) : habitational name from places in Normandy called Gaye, from an early proprietor bearing a Germanic personal name cognate with Wade.probably from the Catalan personal name Gai (Latin Gaius), or in some cases a nickname from Catalan gay ‘cheerful’.Variant of German Gau.North German : from a Frisian personal name Gay.A Congregational clergyman and one of the forerunners of the Unitarian movement in New England, Ebenezer Gay (1696–1787) was born in Dedham, MA, which had been founded by his grandfather, John Gay, who came to America from Wiltshire, England, about 1630 and settled in Watertown, MA. Ebenezer’s great-grandson Howard was editor of the American Anti-Slavery Standard.

    Gay

  • Kalpit
  • Girl/Female

    Indian

    Kalpit

    Imaginary

    Kalpit

  • Humera | حوميرا
  • Girl/Female

    Muslim

    Humera | حوميرا

    The imaginary bird who soars the highest

    Humera | حوميرا

  • Tasavur |
  • Girl/Female

    Muslim

    Tasavur |

    Imaginary picture

    Tasavur |

  • Lincoln
  • Surname or Lastname

    English

    Lincoln

    English : habitational name from the city of Lincoln, so named from an original British name Lindo- ‘lake’ + Latin colonia ‘settlement’, ‘colony’. The place was an important administrative center during the Roman occupation of Britain and in the Middle Ages it was a center for the manufacture of cloth, including the famous ‘Lincoln green’.Abraham Lincoln (1809–65), 16th president of the United States, was the son of an illiterate laborer, descended from a certain Samuel Lincoln, who had emigrated from England to MA in 1637.

    Lincoln

  • Dole
  • Surname or Lastname

    English

    Dole

    English : from Middle English dole ‘portion of land’ (Old English dāl ‘share’, ‘portion’). The term could denote land within the common field, a boundary mark, or a unit of area; so the name may be of topographic origin or a status name.Irish : reduced and altered Anglicized form of McDowell. Compare McDole.French (Dolé) : nickname for a troubled or anxious person, from Old French dolé, past participle of doler ‘to regret’ (Latin dolere ‘to hurt’).

    Dole

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Online names & meanings

  • Zaahirah
  • Girl/Female

    Muslim/Islamic

    Zaahirah

    Guest

  • Havya | ஹவ்யா
  • Girl/Female

    Tamil

    Havya | ஹவ்யா

    To be invoked

  • Vespira
  • Girl/Female

    Latin

    Vespira

    Eveningstar.

  • Luz
  • Girl/Female

    American, Australian, Chinese, French, German, Latin, Spanish

    Luz

    Light

  • Arwarh
  • Boy/Male

    Arabic, Muslim

    Arwarh

    More Delicate; More Gracious

  • Gaurnandanan
  • Boy/Male

    Hindu

    Gaurnandanan

    Lord Murugan

  • CALLAHAN
  • Male

    Irish

    CALLAHAN

    Irish surname transferred to forename use, derived from the personal name Ceallachán, possibly CALLAHAN means "little bright-headed one." 

  • Najaf
  • Boy/Male

    Arabic, Indian, Muslim, Sindhi

    Najaf

    Strong

  • Sampal
  • Boy/Male

    Hindu, Indian

    Sampal

    Equality

  • Shivanne
  • Girl/Female

    Assamese, Hindu, Indian, Kannada, Marathi, Telugu

    Shivanne

    Goddess Parvati

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Other words and meanings similar to

IMAGINARY UNIT

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IMAGINARY UNIT

  • Pseudoblepsis
  • n.

    False or depraved sight; imaginary vision of objects.

  • Amaranth
  • n.

    An imaginary flower supposed never to fade.

  • Imaginate
  • a.

    Imaginative.

  • Sylph
  • n.

    An imaginary being inhabiting the air; a fairy.

  • Imaginary
  • n.

    An imaginary expression or quantity.

  • Imaginant
  • a.

    Imagining; conceiving.

  • Air-drawn
  • a.

    Drawn in air; imaginary.

  • Imaginant
  • n.

    An imaginer.

  • Vision
  • v.

    Hence, something unreal or imaginary; a creation of fancy.

  • Imaginal
  • a.

    Characterized by imagination; imaginative; also, given to the use or rhetorical figures or imagins.

  • Ideal
  • a.

    Imaginary.

  • Imaginer
  • n.

    One who forms ideas or conceptions; one who contrives.

  • Fairyland
  • n.

    The imaginary land or abode of fairies.

  • Imaginariness
  • n.

    The state or quality of being imaginary; unreality.

  • Imaginal
  • a.

    Of or pertaining to an imago.

  • Cocagne
  • n.

    An imaginary country of idleness and luxury.

  • Absolute
  • n.

    In a plane, the two imaginary circular points at infinity; in space of three dimensions, the imaginary circle at infinity.

  • Imaginary
  • a.

    Existing only in imagination or fancy; not real; fancied; visionary; ideal.

  • Imaginarily
  • a.

    In a imaginary manner; in imagination.

  • Fantastic
  • a.

    Existing only in imagination; fanciful; imaginary; not real; chimerical.