Answer
$z=a+bi$, $w=c+di$
So $\frac{}{z} +\frac{}{w}=\frac{}{z+w}$
Work Step by Step
$z=a+bi$, $w=c+di$, prove that $\frac{}{z} +\frac{}{w}=\frac{}{z+w}$
Find the conjugate of the two complex numbers by changing the sign of their imaginary part:
$\frac{}{z}=a-bi$
$\frac{}{w}=c-di$
So $\frac{}{z} +\frac{}{w}=a+c-bi-di$ $(1)$
Evaluate $z+w=a+bi+c+di=a+c+bi+di$
Find the conjugate by changing the sign of the imaginary part of the complex number:
$\frac{}{z+w}=a+c-bi-di$ $(2)$
From $(1)$ and $(2)$, we have: $\frac{}{z} +\frac{}{w}=\frac{}{z+w}$
