Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 377: 43

$Z = 27.4+11.5~i$

$Z_1 = 50+25~i$ $Z_2 = 60+20~i$ $Z = \frac{1}{\frac{1}{Z_1}+\frac{1}{Z_2}}$ $Z = \frac{1}{\frac{Z_2+Z_1}{Z_1~Z_2}}$ $Z = \frac{Z_1~Z_2}{Z_2+Z_1}$ $Z = \frac{(50+25~i)~(60+20~i)}{(60+20~i)+(50+25~i)}$ $Z = \frac{3000-500+1500~i+1000~i}{110+45~i}$ $Z = \frac{2500+2500~i}{110+45~i}~\times~\frac{110-45~i}{110-45~i}$ $Z = \frac{275000+112500+275000~i-112500~i}{14125}$ $Z = \frac{387500+162500~i}{14125}$ $Z = 27.4+11.5~i$