$\frac{2 + 5 i}{3 - 2 i} + \frac{2 - 5 i}{3 + 2 i}$ .

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Solution

$\frac{(2 + 5 i) (3 + 2 i) + (2 - 5 i) (3 - 2 i)}{(3 - 2 i) (3 + 2 i)}$
$\frac{- 4 + 19 i - 4 - 19 i}{13}$
$- \frac{8}{13}$

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