Answer
$10+10i$
Work Step by Step
The given functions are
$f(x)=x-3i$ and $g(x)=4x+2i$.
$\Rightarrow (fg)(x)=f(x)\cdot g(x)$
Substitute both functions.
$\Rightarrow (fg)(x)=(x-3i)\cdot (4x+2i)$
Use the FOIL method.
$\Rightarrow (fg)(x)=4x^2+2xi-12xi-6i^2$
Add like terms.
$\Rightarrow (fg)(x)=4x^2-10xi-6i^2$
Use $i^2=-1$.
$\Rightarrow (fg)(x)=4x^2-10xi+6$
Replace $x$ with $-1$.
$\Rightarrow (fg)(-1)=4(-1)^2-10(-1)i+6$
Simplify.
$\Rightarrow (fg)(-1)=4+10i+6$
Add like terms.
$\Rightarrow (fg)(-1)=10+10i$
