Answer
$18-12i$
Work Step by Step
FOIL the terms in the parentheses, and then combine like terms. Be sure to turn $i^2$ into $-1$.
$(4-i)^2-(1+2i)^2$
$(4-i)(4-i)-(1+2i)(1+2i)$
$16-4i-4i+i^2-(1+2i+2i+4i^2)$
$16-8i-1-(1+4i+4i^2)$
$15-12i-1+4$
$18-12i$
