Question

Simplify :
$\frac{3+2i}{2-5i}+\frac{3-2i}{2+5i}$

Answer 1

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

$=\frac{(3+2i)(2+5i)+(3-2i)(2-5i)}{{\left(2\right)}^2-{\left(5i\right)}^2}$

$=\frac{3(2+5i)+2i(2+5i)+3(2-5i)-2i(2-5i)}{4+5}$

$=\frac{6++15i+4i+10i^2+6-15i-4i+10i^2}{9}$

$=\frac{12+20i^2}{9}$

$=\frac{12-20}{9}$

$=\frac{-8}{9}$