Question

Find the real and imaginary parts of $\frac{4+2i}{1+2i}$.

Answer 1

Real and imaginary part

$\begin{array}{c}\Rightarrow \frac{4+2i}{1+2i}\times \frac{1-2i}{1-2i}\left[\because i^2=1\right]\\ \Rightarrow \frac{4-6i-4i^2}{1-4i^2}\left[\because \left(a-b\right)\left(a+b\right)=a^2-b^2\right]\\ \Rightarrow \frac{4-6i+4}{1+4}=\frac{8-6i}{5}\\ \Rightarrow \frac{8}{5}-\frac{6i}{5}\\ Realpartis\frac{8}{5}\\ Imaginarypart=-\frac{6}{5}i\end{array}$