Chapter 2.16, Problem 7P

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) $Z_1=1-i,Z_2=3i$ (b) $\left|Z_1\right|=3.16,{\theta }_1={18.4}^0;\left|Z_2\right|=4.47,{\theta }_2={63.4}^0$