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...

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...

a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying...

Imaginary Numbers is the fourth EP and seventh release by American rock band The Maine. It was released on December 10, 2013. The EP peaked at number...

Imaginary (psychoanalysis), a concept by Jacques Lacan Imaginary number, a concept in mathematics Imaginary time, a concept in physics Imagination, a mental...

number is called an imaginary number or is referred to as purely imaginary; if the imaginary part is 0, then the number is a real number. Thus the real numbers...

the real numbers, and the vertical y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows for a geometric interpretation...

(such as 10 in decimal, or 2 in binary) as their bases, it uses the imaginary number 2 i {\displaystyle 2i} (such that ( 2 i ) 2 = − 4 {\displaystyle (2i)^{2}=-4}...

In algebraic number theory, a number field is called totally imaginary (or totally complex) if it cannot be embedded in the real numbers. Specific examples...

e. the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number. Mass versus weight Effective...

Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic...

A number which is a direct multiple of i {\displaystyle i} is known as an imaginary number.: Chp 4  A number that is the sum of an imaginary number and...

quadratic field, and, if d < 0 {\displaystyle d<0} , it is called an imaginary quadratic field or a complex quadratic field, corresponding to whether...

mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that the...

space by means of a transformation that substitutes an imaginary-number variable for a real-number variable. Wick rotations are useful because of an analogy...

rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number). In some modern formulations of the theory...

In number theory, the Heegner theorem[inconsistent] establishes the complete list of the quadratic imaginary number fields whose rings of integers are...

the rules of the formal system in which it is used. For example, the imaginary number − 1 {\displaystyle {\sqrt {-1}}} is undefined within the set of real...

In complex geometry, an imaginary line is a straight line that only contains one real point. It can be proven that this point is the intersection point...

adjoining the imaginary number i to the field of rationals Q. The field of Gaussian rationals provides an example of an algebraic number field that is...

Relative permittivity is a dimensionless number that is in general complex-valued; its real and imaginary parts are denoted as: ε r ( ω ) = ε r ′ ( ω...

equations. Every holomorphic function can be separated into its real and imaginary parts ⁠ f ( x + i y ) = u ( x , y ) + i v ( x , y ) {\displaystyle f(x+iy)=u(x...

is 32-bit float) and complex128 (each component is 64-bit float). Imaginary number literals can be specified by appending an "i". The Perl core module...

linear sizes. In complex numbers, the cube of a purely imaginary number is also purely imaginary. For example, i3 = −i. The derivative of x3 equals 3x2...

having a value that is an imaginary number with units of length). It is customary when charge radius takes an imaginary numbered value to report the negative...

degree two. Any number field that is Galois over the rationals must be either totally real or totally imaginary. Totally imaginary number field CM-field...

Imaginary friends (also known as pretend friends, invisible friends or made-up friends) are a psychological and a social phenomenon where a friendship...

same number ( 31 8 = 25 10 {\displaystyle 31_{8}=25_{10}} ). Some jokes are based on imaginary number i, treating it as if it is a real number. A telephone...

j\phi =j\left(\beta -\alpha \right)} Where: j {\displaystyle j} is the imaginary number β {\displaystyle \beta } is the phase of the magnetomotive force α...

Roman numeral I represents the number 1. In mathematics, a lowercase "i" is used to represent the unit imaginary number, while an uppercase "I" serves...