Answer
$\frac{1}{5}+\frac{11}{10}i$
Work Step by Step
$\frac{3+4i}{4-2i}$
Multiply Numerator and Denominator by $4+2i$
$=\frac{3+4i}{4-2i} \times \frac{4+2i}{4+2i}$
$=\frac{(3+4i)(4+2i)}{(4-2i)(4+2i)} $
Using $(a+b)(a-b)=a^{2}-b^{2}$
$=\frac{12+16i+6i+8i^{2}}{4^{2}-(2i)^{2}} $
$=\frac{12+22i+8i^{2}}{16-4i^{2}} $
$=\frac{12+22i+8(-1)}{16-4(-1)} $ [Using $i^{2}=-1$]
$=\frac{12+22i-8}{16+4} $
$=\frac{4+22i}{20} $
$=\frac{4}{20} +\frac{22i}{20} $
$=\frac{1}{5} +\frac{11}{10}i $
