Answer
$4-i$
Work Step by Step
Step 1: Multiplying the expression by the complex conjugate of the
denominator in both the numerator and the denominator:
$\frac{14+5i}{3+2i}\times\frac{3-2i}{3-2i}$
Step 2: $\frac{14+5i}{3+2i}\times\frac{3-2i}{3-2i}=\frac{(14+5i)(3-2i)}{(3)^{2}-(2i)^{2}}$
Step 3: $\frac{(14+5i)(3-2i)}{(3)^{2}-(2i)^{2}}=\frac{42-28i+15i-10i^{2}}{9-4i^{2}}=\frac{42-13i-10(-1)}{9-4(-1)}$
Step 4: $\frac{42-13i-10(-1)}{9-4(-1)}=\frac{42-13i+10}{13}=\frac{52-13i}{13}$
Step 5: $\frac{52-13i}{13}=\frac{13(4-i)}{13}=4-i$