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A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and ...

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...

A vector whose elements are complex numbers.

A complex vector bundle is a vector bundle pi:E->M whose fiber bundle pi^(-1)(x) is a complex vector space. It is not necessarily a complex manifold, even if its base ...

Complex infinity is an infinite number in the complex plane whose complex argument is unknown or undefined. Complex infinity may be returned by the Wolfram Language, where it ...

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

The difference of two complex numbers z=x+iy and z^'=x^'+iy^' is given by z-z^'=(x-x^')+i(y-y^'). In component form, (x,y)-(x^',y^')=(x-x^',y-y^').

A complex vector space is a vector space whose field of scalars is the complex numbers. A linear transformation between complex vector spaces is given by a matrix with ...