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A directed infinity in direction z is an infinite numerical quantity that is a positive real multiple of the complex number z. Directed infinity may be returned in the ...

A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

Every nonconstant entire function attains every complex value with at most one exception (Henrici 1988, p. 216; Apostol 1997). Furthermore, every analytic function assumes ...

A complex number z is said to be purely imaginary if it has no real part, i.e., R[z]=0. The term is often used in preference to the simpler "imaginary" in situations where z ...

The word "place" has a special meaning in complex variables, where it roughly corresponds to a point in the complex plane (except that it reflects the Riemann sheet structure ...

A disk with radius 1. The (open) unit disk can also be considered to be the region in the complex plane defined by {z:|z|<1}, where |z| denotes the complex modulus. (The ...

The absolute square of a complex number z, also known as the squared norm, is defined as |z|^2=zz^_, (1) where z^_ denotes the complex conjugate of z and |z| is the complex ...

An abstract simplicial complex is a collection S of finite nonempty sets such that if A is an element of S, then so is every nonempty subset of A (Munkres 1993, p. 15).

An antilinear operator A^~ satisfies the following two properties: A^~[f_1(x)+f_2(x)] = A^~f_1(x)+A^~f_2(x) (1) A^~cf(x) = c^_A^~f(x), (2) where c^_ is the complex conjugate ...

An Argand diagram is a plot of complex numbers as points z=x+iy in the complex plane using the x-axis as the real axis and y-axis as the imaginary axis. In the plot above, ...