#### Answer

$-1-2i$

#### Work Step by Step

Multiply the numerator and denominator by the conjugate of the complex imaginary number.
$\frac{(1-3i)}{(1+i)}\times\frac{(1-i)}{(1-i)}$
Use foil to expand numerator; use the difference of two squares to expand the denominator.
$\frac{1-i-3i+3i^2}{1-i^2}$
Remember that $i^2=-1$.
$\frac{1-4i-3}{1+1}$
Combine like terms in both numerator and denominator.
$\frac{-2-4i}{2}$
Separate.
$-1-2i$