#### Answer

$-\frac{3}{2}+\frac{5}{2}i$

#### Work Step by Step

$\frac{1+4i}{1-i}\times\frac{1+i}{1+i}$
=$\frac{(1+4i)(1+i)}{(1-i)(1+i)}$
=$\frac{1(1+i)+4i(1+i)}{(1)^{2}-(i)^{2}}$
=$\frac{1+i+4i+4i^{2}}{1-(-1)}$
=$\frac{1+5i+4(-1)}{2}$
=$\frac{1-4+5i}{2}$
=$\frac{-3+5i}{2}$
=$-\frac{3}{2}+\frac{5}{2}i$