Answer
$-\frac{3}{26}+\frac{11i}{26}$
Work Step by Step
Step 1: Multiplying both the numerator and the denominator by the complex conjugate of the denominator:
$\frac{2+i}{1-5i}\times\frac{1+5i}{1+5i}$
Step 2: $\frac{(2+i)(1+5i)}{(1-5i)(1+5i)}=\frac{2(1+5i)+i(1+5i)}{(1)^{2}-(5i)^{2}}=\frac{2+10i+i+5i^{2}}{1-25i^{2}}$
Step 3: $\frac{2+10i+i+5i^{2}}{1-25i^{2}}=\frac{2+11i+5(-1)}{1-25(-1)}=\frac{2+11i-5}{26}$
Step 4: $\frac{2+11i-5}{26}=\frac{-3+11i}{26}=-\frac{3}{26}+\frac{11i}{26}$
