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Complex Analysis

A complex polynomial is a polynomial with complex coefficients.

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

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 vector whose elements are complex numbers.

A variable that may assume complex values.

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

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 ...

A complex number may be taken to the power of another complex number. In particular, complex exponentiation satisfies (a+bi)^(c+di)=(a^2+b^2)^((c+id)/2)e^(i(c+id)arg(a+ib)), ...