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Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1. In mathematics, 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 the equation =; every complex number can be expressed in the form ...
Geometry of Complex Numbers is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean geometry. It was written by Hans Schwerdtfeger , and originally published in 1962 as Volume 13 of the Mathematical Expositions series of the University of Toronto Press .
x is the argument of the complex number (angle between line to point and x-axis in polar form). The notation is less commonly used in mathematics than Euler's formula , e ix , which offers an even shorter notation for cos x + i sin x , but cis(x) is widely used as a name for this function in software libraries .
In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra of a complex vector space. [1] The special case of a 1-dimensional algebra is known as a dual number .
A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized by the angle measure : = = + . This is the exponential map for the circle group.
Binary coding systems of complex numbers, i.e. systems with the digits = {,}, are of practical interest. [9] Listed below are some coding systems , (all are special cases of the systems above) and resp. codes for the (decimal) numbers −1, 2, −2, i. The standard binary (which requires a sign, first line) and the "negabinary" systems (second ...
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