1. Compute $i+i^2+i^3+\cdots+i^{2016}+i^{2017}$.
2. Find a complex number $z$ such that the real part and imaginary part of $z$ are both integers, and such that$$z\overline z = 89.$$
3. Simplify $(1+i)^{2016}-(1-i)^{2016}$.
4. Express $\frac 1{1+\frac 1{1-\frac 1{1+i}}}$ in the form $a+bi$, where $a$ and $b$ are real numbers.
