Answer
$2-2i$
Work Step by Step
Multiply the numerator and denominator by the conjugate of the complex imaginary number.
$\frac{(6+2i)}{(2+2i)}\times\frac{(1-2i)}{(1-2i)}$
Use foil to expand numerator; use the difference of two squares to expand the denominator.
$\frac{6-12i+2i-4i^2}{1-4i^2}$
Remember that $i^2=-1$.
$\frac{6-10i+4}{1+4}$
Combine like terms in both numerator and denominator.
$\frac{10-10i}{5}$
Simplify. Divide both by 5.
$2-2i$
