See @fog856 the domain of all trigonometric functions and their general solutions, are defined only for real values of the angle that you put into them. That is you could say
x=n\pi+y only for real values of y and x
Also you said about polar form.
Yes it’s true that every complex number can be represented in trigonometric format:
cos\theta+isin\theta but here also you keep in only real values of \theta.
Any further doubts,do let me know