linguistic:voice_change
Complex-valued function of several real variables

A complex-valued function of several real variables may be defined by relaxing, in the definition of the real-valued functions, the restriction of the codomain to the real numbers, and allowing complex values.

If f (x, …, x) is such a complex valued function, it may be decomposed as

where g and h are real-valued functions. In other words, the study of the complex valued functions reduces easily to the study of the pairs of real valued functions.

This reduction works for the general properties. However, for an explicitly given function, such as:

the computation of the real and the imaginary part may be difficult.