Answer
$18-12i$.
Work Step by Step
The given expression is
$=(4-i)^2-(1+2i)^2$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
We have $A=(4-i)$ and $B=(1+2i)$.
$=[(4-i)-(1+2i)][(4-i)+(1+2i)]$
Clear the parentheses.
$=[4-i-1-2i][4-i+1+2i]$
Add like terms.
$=[3-3i][5+i]$
Use the FOIL method.
$=15+3i-15i-3i^2$
Use $i^2=-1$.
$=15+3i-15i+3$
Add like terms
$=18-12i$.
