Search Results for ""

Complex Analysis

The complex conjugate of a complex number z=a+bi is defined to be z^_=a-bi. (1) The conjugate matrix of a matrix A=(a_(ij)) is the matrix obtained by replacing each element ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

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

A vector whose elements are complex numbers.

A variable that may assume complex values.

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 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^').