Answer
$-\frac{3}{2}-\frac{7i}{2}$
Work Step by Step
Step 1: Multiplying both the numerator and the denominator by the complex conjugate of the denominator:
$\frac{2-5i}{1+i}\times\frac{1-i}{1-i}$
Step 2: $\frac{(2-5i)(1-i)}{(1+i)(1-i)}=\frac{2(1-i)-5i(1-i)}{(1)^{2}-(i)^{2}}=\frac{2-2i-5i+5i^{2}}{1-(-1)}$
Step 3: $\frac{2-2i-5i+5i^{2}}{1-(-1)}=\frac{2-7i+5(-1)}{1+1}=\frac{2-7i-5}{2}$
Step 4: $\frac{2-7i-5}{2}=\frac{-3-7i}{2}=-\frac{3}{2}-\frac{7i}{2}$
