Answer
$-\dfrac{7}{3}+\dfrac{4}{3}i$
Work Step by Step
Multiply both the numerator and the denominator by the conjugate of the denominator, which is $3i$, to obtain:
$=\dfrac{(4+7i)(3i)}{-3i(3i)}
\\=\dfrac{12i+21i^2}{-9i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{12i+21(-1)}{-9(-1)}
\\=\dfrac{12i-21}{9}
\\=\dfrac{-21+12i}{9}
\\=-\dfrac{21}{9} + \dfrac{12}{9}i
\\=-\dfrac{7}{3}+\dfrac{4}{3}i$
