Solve for: (5-2i)/(4+2i)

Expression: $\frac{5-2i}{4+2i}$

Multiply by the conjugate $ \frac{4-2i}{4-2i}$

$=\frac{(5-2i)(4-2i)}{(4+2i)(4-2i)}$

Simplify $\frac{(5-2i)(4-2i)}{(4+2i)(4-2i)}:{\quad}\frac{16-18i}{20}$

$=\frac{16-18i}{20}$

Apply the fraction rule $\frac{a+bi}{c}=\frac{a}{c}+\frac{b}{c}i$

$=\frac{16}{20}+\frac{-18}{20}i$

Simplify $\frac{16}{20}+\frac{-18}{20}i:{\quad}\frac{4}{5}-\frac{9}{10}i$

$=\frac{4}{5}-\frac{9}{10}i$