Answer
$-1-2i$
Work Step by Step
Step 1: Multiplying both the numerator and the denominator of the expression by the complex conjugate of the denominator:
$\frac{1-3i}{1+i}\times\frac{1-i}{1-i}$
Step 2: $\frac{1-3i}{1+i}\times\frac{1-i}{1-i}=\frac{(1-3i)(1-i)}{(1)^{2}-(i)^{2}}$
Step 3: $\frac{(1-3i)(1-i)}{(1)^{2}-(i)^{2}}=\frac{1-i-3i+3i^{2}}{1+1}=\frac{1-4i+3(-1)}{2}$
Step 4: $\frac{1-4i+3(-1)}{2}=\frac{1-4i-3}{2}=\frac{-2-4i}{2}=-1-2i$