## College Algebra (11th Edition)

$-1-2i$
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. $-1-2i$