"i (number)" redirects here. For internet numbers, see i-number.
The imaginary unit i in the complex plane: Real numbers are conventionally drawn on the horizontal axis, and imaginary numbers on the vertical axis.
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i.
Imaginary numbers are an important mathematical concept; they extend the real number system to the complex number system in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square.
There are two complex square roots of −1:i and −i, just as there are two complex square roots of every real number other than zero (which has one double square root).
In contexts in which use of the letter i is ambiguous or problematic, the letter j is sometimes used instead. For example, in electrical engineering and control systems engineering, the imaginary unit is normally denoted by j instead of i, because i is commonly used to denote electric current.[1]
^Stubbings, George Wilfred (1945). Elementary vectors for electrical engineers. London: I. Pitman. p. 69. Boas, Mary L. (2006). Mathematical Methods in the Physical Sciences (3rd ed.). New York [u.a.]: Wiley. p. 49. ISBN 0-471-19826-9.
The imaginaryunit or unitimaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property...
An imaginary number is a real number multiplied by the imaginaryunit i, which is defined by its property i2 = −1. The square of an imaginary number bi...
extends the real numbers with a specific element denoted i, called the imaginaryunit 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 imaginaryunit i. Imaginary time is...
increasingly precise digits of π is a world record pursuit. The imaginaryunit or unitimaginary number, denoted as i, is a mathematical concept which extends...
the SI derived unit for energy. In some areas of physics, electrical engineering and related fields, j is the symbol for the imaginaryunit (the square root...
{\displaystyle \operatorname {erfi} z=-i\operatorname {erf} iz,} where i is the imaginaryunit. The name "error function" and its abbreviation erf were proposed by...
value of a function, the letter i {\displaystyle i} to express the imaginaryunit − 1 {\displaystyle {\sqrt {-1}}} , the Greek letter Σ {\displaystyle...
difference between voltage and current. j {\displaystyle j} is the imaginaryunit, and is used instead of i {\displaystyle i} in this context to avoid...
the complex numbers 1/2 + i t, where t is a real number and i is the imaginaryunit. The Riemann zeta function is defined for complex s with real part greater...
The symbol i in mathematical equations may refer to; Imaginaryunit (i), for which i2 = -1 Imaginary number Complex number i, an index variable in a matrix...
complex numbers as a plane, the multiplication of a complex number by the imaginaryunit i=√-1 is equivalent to counter-clockwise rotating the vector representing...
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 imaginaryunit. In this...
real anti-symmetric matrix is multiplied by a real multiple of the imaginaryunit i , {\displaystyle i,} then it becomes Hermitian. Every Hermitian matrix...
System of Units ISO 31 Elert, Glenn. "Special Symbols". The Physics Hypertextbook. Retrieved 4 August 2021. NIST (16 August 2023). "SI Units". www.nist...
{\partial }{\partial x}}} where ħ is Planck's reduced constant, i the imaginaryunit, x is the spatial coordinate, and a partial derivative (denoted by ∂...
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...
term "sign convention" is used more broadly to include factors of the imaginaryunit i and 2π, rather than just choices of sign. In relativity, the metric...
using complex numbers, S = P + j Q (where j is the imaginaryunit). The formula for complex power (units: VA) in phasor form is: S = V I ∗ = | S | ∠ φ {\displaystyle...
written as U = eiH, where e indicates the matrix exponential, i is the imaginaryunit, and H is a Hermitian matrix. For any nonnegative integer n, the set...
numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginaryunit i {\displaystyle i} , where i...
form where Ek is the (constant) complex amplitude vector, i is the imaginaryunit, k is the wave vector (whose magnitude k is the angular wavenumber)...
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