complex analysis - How do I find the real and imaginary part of $z+ e^z$

How can I find the imaginary and real part of $z + e^z$ ?

I tried but I only get

$$x + yi + e^x e^{yi}$$

Answer

HINT:

You are on the right track. Note that $e^{iy}=\cos(y)+i\sin(y)$.