Answer
$\dfrac{28}{25} + \dfrac{21}{25}i$
Work Step by Step
Multiply both the numerator and the denominator by the conjugate of the denominator, which is $4+3i$, to obtain:
$=\dfrac{7(4+3i)}{(4-3i)(4+3i)}
\\=\dfrac{28+21i}{(4-3i)(4+3i)}$
Simplify using the rule $(a-b)(a+b)=a^2-b^2$ to obtain:
$=\dfrac{28+21i}{4^2-(3i)^2}
\\=\dfrac{28+21i}{16-9i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{28+21i}{16-9(-1)}
\\=\dfrac{28+21i}{16+9}
\\=\dfrac{28+21i}{25}
\\=\dfrac{28}{25} + \dfrac{21}{25}i$
