The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x2 + 1 = 0. Although there is no...

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...

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} ; every...

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...

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

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

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...

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

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...

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...

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

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...

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....

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...

numbers and the hyperbolic unit j satisfies j 2 = + 1 {\displaystyle j^{2}=+1} In the field of complex numbers the imaginary unit i satisfies i 2 = − 1. {\displaystyle...

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...

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...

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...

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...

{\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 ∂...

real anti-symmetric matrix is multiplied by a real multiple of the imaginary unit i , {\displaystyle i,} then it becomes Hermitian. Every Hermitian matrix...

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...

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

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...

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...

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

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...

of 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 general,...

-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...

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)...