Answer
$-1-31i$
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:
$=7(2-3i) - 5i(2-3i)
\\=7(2) - 7(3i) - 5i(2) + 5i(3i)
\\=14 - 21i - 10i +15i^2
\\=14 - 31i + 15i^2$
Use rule (2) above to obtain:
$=14-31i+15(-1)
\\=14-31i+(-15)
\\=14-31i-15
\\=-1-31i$
