#### Answer

(a) $\frac{41}{25}-\frac{12}{25}i$
(b) $-20$

#### Work Step by Step

(a) We multiply the numerator and denominator by the conjugate:
$\frac{8+3i}{4+3i}=\frac{8+3i}{4+3i}*\frac{4-3i}{4-3i}=\frac{32-12i-9i^{2}}{16-9i^{2}}=\frac{32-12i-9*-1}{16--9}=\frac{32-12i+9}{16+9}=\frac{41-12i}{25}=\frac{41}{25}-\frac{12}{25}i$
(b) $\sqrt{-10}*\sqrt{-40}=\sqrt{10}i* 2\sqrt{10}i=20i^{2}=-20$