Answer
$7+19i$
Work Step by Step
RECALL:
(1)
$(a+b)(c+d)
\\= a(c+d) + b(c+d)
\\=ac+ad + bc + bd$
(2) $i^2=-1$
Use rule (1) above to obtain:
$=3(4+5i) + i(4+5i)
\\=3(4) + 3(5i) + i(4) + i(5i)
\\=12+ 15i+4i+5i^2
\\=12 + 19i+5i^2$
Use rule (2) above to obtain:
$=12+19i+5(-1)
\\=12+19i+(-5)
\\=12+19i-5
\\=7+19i$
