Answer
$\frac{3}{13}-\frac{11i}{13}$
Work Step by Step
Complex numbers are divided by multiplying the numerator and
denominator by the complex conjugate of the denominator:
Step 1: $\frac{2-4i}{5+i}\times\frac{5-i}{5-i}$
Step 2: $\frac{(2-4i)(5-i)}{(5+i)(5-i)}$
Step 3: $\frac{2(5-i)-4i(5-i)}{5(5-i)+i(5-i)}$
Step 4: $\frac{10-2i-20i+4i^{2}}{25-5i+5i-i^{2}}$
Step 5: $\frac{10-22i+4i^{2}}{25-i^{2}}$
Step 6: $\frac{10-22i+4(-1)}{25-(-1)}$
Step 7: $\frac{10-22i-4}{25+1}$
Step 8: $\frac{6-22i}{26}$
Step 9: $\frac{6}{26}-\frac{22i}{26}$
Step 10: $\frac{3}{13}-\frac{11i}{13}$
The answer is in rectangular form.
