Answer
(a) $ 5-8i$
(b) $ -29-3i$
(c) $ 55+48i$
(d) $ 6+i$
Work Step by Step
Use the property $i^2=-1$, we have:
(a) $(9-3i)-(4+5i)=9-3i-4-5i=5-8i$
(b) $(4+3i)(-5+3i)=-20+12i-15i-9=-29-3i$
(c) $(8+3i)^2=64+48i-9=55+48i$
(d) $\frac{3+19i}{1+3i}=\frac{3+19i}{1+3i}\times\frac{1-3i}{1-3i}=\frac{3-9i+19i+57}{1+9}=\frac{60+10i}{10}=6+i$
