Functions for complex numbers in GLSL. https://www.shadertoy.com/

complex.frag

vec2 cmpxcjg(in vec2 c) {
	return vec2(c.x, -c.y);
}

vec2 cmpxmul(in vec2 a, in vec2 b) {
	return vec2(a.x * b.x - a.y * b.y, a.y * b.x + a.x * b.y);
}

vec2 cmpxpow(in vec2 c, int p) {
	for (int i = 0; i < p; ++i) {
		c = cmpxmul(c, c);
	}
    return c;
}

vec2 cmpxdiv(in vec2 a, in vec2 b) {
    return cmpxmul(a, cmpxcjg(b));
}

float cmpxmag(in vec2 c) {
    return sqrt(c.x * c.x + c.y * c.y);
}

Hello,
the cmpxpow function is rong, is should read something like:
vec2 cmpxpow(in vec2 c, int p) {
vec2 tmp = vec2(1.0,0.0) ;
for (int i = 0; i < p; ++i) {
c = cmpxmul(tmp, c);
}
return c;
}

Cheers,
Paulo