A geometric description would be that it rotates z by an angle of theta in the counter clockwise direction. Correct?
Writing function in polar can I say -
$f(z) = e^{i\theta}re^{i\theta}$
or should that be -
$f(z) = e^{i\theta}re^{i\gamma}$
I know the $\theta$ is used in the definition of a complex number in polar form , $re^{i\theta}$, but it looks like in this case it is 'already taken' by the first number ($e^{i\theta}$)...or maybe the question means for me to use in the second number too? Or do I even need to bother writing out this stuff, will the once line answer above suffice?