You can use de Moivre's formula.
Just know that with a real power, you may (will?) find two values for z.
If I remember correctly (and I hope I do, because I have an exam on this next week
), it goes something like this:
| c++: |
float r, i; // real, imaginary components of base float p; // power // convert to polar form float t, b; // angle, distance from (0, 0) b = sqrt((r * r) + (i * i)); // Pythagorean theorem t = arctan(i / r); // assuming range of (-pi / 2, pi / 2) for arctan if(r < 0){ t = pi - t; } if(i < 0){ t = (2 * pi) - t; } // raise to power t = t * p; b = pow(b, p); // if there is more than one value, I think you could just take -b here and do the same stuff with it that is done below to get it the other // put back in rectangular form r = b * cos(t); i = b * sin(t); |
I really have a feeling that I made a mistake or two so that code could use some testing before it gets any use, but it should at least demonstrate how it works.