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A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
The complex numbers contain a number i, the imaginary unit, with i 2 = −1, i.e., i is a square root of −1. Every complex number can be represented in the form x + iy, where x and y are real numbers called the real part and the imaginary part of the complex number respectively.
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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 .
In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space V C over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers.
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 .
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