Question

Express the complex number $\frac{2+i}{3-4i}$ in $a+ib$ form.

Answer 1

Given the complex number is

$\frac{2+i}{3-4i}$ $=\frac{(2+i)(3+4i)}{3^2-16i^2}$

$=\frac{2+11i}{25}$

$=\frac{2}{25}+i\frac{11}{25}$.

This is the required $a+ib$ form.