You can and should visualize imaginary and complex numbers. Whoever told you otherwise was wrong. See my other post. Plot a complex number (say 2+4i) and then try two operations on it: multiply by 2+2i (this will rotate the point to the left and scale it); and try adding a complex number (say 1-3i) which will have the effect of translating the original point.

Developing an intuition about what rotation a particular complex number will give you is more complex, admittedly. But this is enough to visualize the effects, if not precisely mentally predict the result.