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.

## Complex Power FunctionEdit

### IntroductionEdit

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 "i^{2} = -1 ".

Complex power is defined by the mathematical operation of exponentiation given by "z_{1}^{z2}" .

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

#### Header FileEdit

Standard Library Header file : <complex.h>(complex arithmetic)

#### Syntax for functionEdit

double complex cpow(double complex x, double complex y);

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, e^{ia} = (cos a +i sin a).Here,cos and sin are trigonometric functions.

For x^{ia},

x^{i .a} = e^{i .a ln(x)} = ( cos(a ln(x)) + i sin(a ln(x)) ) ; ln : logarithmic function to the base e.

#### Return ValueEdit

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.

### Usage of Cpow functionEdit

//Program returns the complex number z3 #include<stdio.h> #include<complex.h> #include<math.h> int main() { int x, y, p, q; double complex z1, z2, z3; //complex variables declaration scanf("%d %d %d %d", &x, &y, &p, &q); z1 = (p + q * I); z2 = (x + y * I); z3 = cpow (z2, z1); printf("%f + %f * i\n", creal(z3), cimag(z3)); return 0; }