C Programming/complex.h/cpow

Description
Cpow is a library function in the C programming language, used to calculate powers in the field of complex numbers

It was added to the C programming language, together with complex number support, in the C99 standard.

Introduction
In mathematics, complex numbers are often denoted by 'z'. z = x + iy In this number 'x' is the real part and 'y' is imaginary part. 'i' is imaginary unit, such that "i2 = -1 ".

Complex power is defined by the mathematical operation of exponentiation given by "z1z2".

In C programming language, library function for this is given by Cpow.

Header File
Standard Library Header file : (complex arithmetic)

Syntax for function
This function calculates the power of real number 'x' raised to y-th power ,where y is a complex number.

In mathematics ,by Euler's formula, eia = (cos a +i sin a).Here,cos and sin are trigonometric functions.

For xia,

xi .a = ei .a ln(x) = ( cos(a ln(x)) + i sin(a ln(x)) ) ;  ln  : logarithmic function to the base e.

Return Value
This function shall return the complex power function value. Returns the complex power of base x raised to the y-th power using the principal branch, whose cuts are along the negative real axis.