Answer
$\dfrac{4}{5}-\dfrac{3}{5}i$
Work Step by Step
Multiply both the numerator and the denominator by the conjugate of the denominator, which is $-5i$, to obtain:
$=\dfrac{(3+4i)(-5i)}{5i(-5i)}
\\=\dfrac{-15i-20i^2}{-25i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{-15i-20(-1)}{-25(-1)}
\\=\dfrac{-15i+20}{25}
\\=\dfrac{20-15i}{25}
\\=\dfrac{20}{25} - \dfrac{15}{25}i
\\=\dfrac{4}{5}-\dfrac{3}{5}i$
