Answer
$\dfrac{14+5i}{3+2i}=4-i$
Work Step by Step
$\dfrac{14+5i}{3+2i}$
Begin the evaluation of the quotient by multiplying the numerator and the denominator by the complex conjugate of the denominator:
$\dfrac{14+5i}{3+2i}\cdot\dfrac{3-2i}{3-2i}=\dfrac{(14+5i)(3-2i)}{3^{2}-(2i)^{2}}=...$
Evaluate the operations indicated in the numerator and in the denominator:
$...=\dfrac{42-28i+15i-10i^{2}}{9-4i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{42-28i+15i-10(-1)}{9-4(-1)}=\dfrac{42-13i+10}{9+4}=...$
$...=\dfrac{52-13i}{13}=\dfrac{52}{13}-\dfrac{13}{13}i=4-i$
