I'm having trouble calculating following (complex) integral. $$\int_D z^n dA$$ where $D=\{ z \in \mathbb{C} \mid \lvert z \rvert \leq 1 \}$.
I know how to calculate complex (line) integrals and real double integrals but I'm having difficulties combining those.
Hint: Using polar coordinates the integrand is $$z^n=r^n e^{in \theta} $$ and the area element becomes $$dA=rdrd \theta. $$
The limits of integration should be obvious.