Chapter 2.16, Problem 6P

In electricity we learn that the resistance of two resistors in series is $R_1+R_2$ and the resistance of two resistors in parallel is ${(R_1{}^{-1}+R_2{}^{-1})}^{-1}$.

Corresponding formulas hold for complex impedances. Find the impedance of $Z_1$ and $Z_2$ in series, and in parallel, given:

(a) $Z_1=2+3i,Z_2=1-5i$ (b) $Z_1=2\sqrt{3}{e}^{i\pi /6},Z_2=2e^{2i\pi /3}$