>>12083267A complex power introduces two degrees of freedom when you apply it to an argument. Every complex number on the complex plane has a "modulus" which can be thought of in exactly the same terms as the magnitude of a vector, and it's a real number. Particularly, the real numbers are their own moduli, but this is not necessarily true for the complex. Additionally there is an factor to the complex power which is given by euler's formula, and it tells us that when theta is 1, you have a 180 degree counterclockwise rotation in the output, but by changing theta, you can change the amount of rotation. The modulus will just act like any real power. Put the two together and you get a stretching and rotating effect on any number that you raise to a complex power. as a power acts like certain linear transformations which act on , notably the rotations and the dilations.
