Answer
$\theta = 22.8^{\circ}$
Work Step by Step
$Z_1 = 50+25~i$
$Z_2 = 60+20~i$
$Z = \frac{1}{\frac{1}{Z_1}+\frac{1}{Z_2}}$
$Z = \frac{1}{\frac{Z_2+Z_1}{Z_1~Z_2}}$
$Z = \frac{Z_1~Z_2}{Z_2+Z_1}$
$Z = \frac{(50+25~i)~(60+20~i)}{(60+20~i)+(50+25~i)}$
$Z = \frac{3000-500+1500~i+1000~i}{110+45~i}$
$Z = \frac{2500+2500~i}{110+45~i}~\times~\frac{110-45~i}{110-45~i}$
$Z = \frac{275000+112500+275000~i-112500~i}{14125}$
$Z = \frac{387500+162500~i}{14125}$
$Z = 27.4+11.5~i$
We can find the angle $\theta$:
$tan~\theta = \frac{11.5}{27.4}$
$\theta = arctan(\frac{11.5}{27.4})$
$\theta = 22.8^{\circ}$
