Answer
$\dfrac{5}{3-2i}=\dfrac{15}{13}+\dfrac{10}{13}i$
Work Step by Step
$\dfrac{5}{3-2i}$
Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator:
$\dfrac{5}{3-2i}=\dfrac{5}{3-2i}\cdot\dfrac{3+2i}{3+2i}=\dfrac{5(3+2i)}{3^{2}-(2i)^{2}}=\dfrac{5(3+2i)}{9-4i^{2}}=...$
Substitute $i^{2}$ with $-1$ and simplify:
$...=\dfrac{5(3+2i)}{9-4(-1)}=\dfrac{5(3+2i)}{9+4}=\dfrac{15+10i}{13}=\dfrac{15}{13}+\dfrac{10}{13}i$
