Answer
$\frac{8}{5}+\frac{16}{5}i$.
Work Step by Step
$=\frac{8}{1+\frac{2}{i}}$
$=\frac{8}{\frac{i}{i}+\frac{2}{i}}$
Add numerators because denominators are the same.
$=\frac{8}{\frac{i+2}{i}}$
Invert the divisor and multiply.
$=\frac{8i}{2+i}$
The conjugate of the denominator is $2-i$.
Multiply the numerator and the denominator by $2-i$.
$=\frac{8i}{2+i}\cdot \frac{2-i}{2-i}$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
Use $i^2=-1$.
$=\frac{16i+8}{4+1}$
Simplify.
$=\frac{16i+8}{5}$
Rewrite as $a+ib$.
$=\frac{8}{5}+\frac{16}{5}i$.
