Question

Find the real and imaginary part of $\frac{3-2i}{7+4i}$

Answer 1

Let$z_1=\frac{3-2i}{7+4i}$

Multiplying and dividing $z_1$ by $7-4i$

We get,

$z_1=\frac{(3-2i)(7-4i)}{(7+4i)(7-4i)}$

$=\frac{21-12i-14i-8}{7^2+4^2}$

$=\frac{13-26i}{65}$

$z_1=\frac{1-2i}{5}$

$z_1=\frac{1}{5}+\frac{-2i}{5}$

Comparing with $z=x+iy$

We get,

Real part $=\frac{1}{5}$

Imaginary part $=\frac{-2}{5}$