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There is no standard library files in C Programming which can do complex number calculations. According to bionomial theoram there can be Complex and Real roots. But as C doesn’t bother with Complex numbers so, we need to use real number canculation to get the complex root at a+bi form.

Here is a short example what i have done:

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#include <stdio.h>
#include <math.h>
#include <conio.h>
void main()
{
double a,b,c,d,e,f,g;
clrscr();
printf("Please type the numbers");
scanf("%lf%lf%lf",&a,&b,&c);
 
d=(b*b)-(4*a*c);
 
if (d>=0) {
	if (d==0) {
	printf("It has one real root\n");
	e=(-b+sqrt(d))/(2*a);
	printf("Here is the root: %.2lf\n",e);
		} else {
	printf("It has real roots\n");
	e=(-b+sqrt(d))/(2*a);
	printf("First Real Root: %.2lf\n",e);
	e=(-b-sqrt(d))/(2*a);
	printf("Second Real Root: %.2lf\n",e);
	}
} else {
	printf("It has complex roots\n");
	f=-d;
	e=(-b/(2*a));
	g=(sqrt(f)/(2*a));
	printf("First Complex Root: %.2lf+%.2lfi\n",e,g);
	printf("Second Complex Root: %.2lf-%.2lfi\n",e,g);
	}
getch();
 
}

If you enter some value for this programme like 1 3 1 for a,b and c according to a Quadratic or Bionomial Equation then the result will be with two real number outputs. If you enter 1 2 1 for a,b and c then the result will be one real number output as at that time both roots will be equal. And if you enter 1 1 1 then the result will be with two complex numbers.

Happy Coding!