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  4. The real part of ((1+i)2/(3-i)) is

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Q. The real part of $\frac{\left(1+i\right)^{2}}{\left(3-i\right)}$ is

Complex Numbers and Quadratic Equations

Solution:

$\left(1+i\right)^{2}=1+i^{2}+2i=2i$
$\therefore \, \frac{\left(1+i\right)^{2}}{3-i}$
$=\frac{2i\left(3+i\right)}{3^{2}-i^{2}}$
$=\frac{6i-2}{10}$
$=\frac{-1+3i}{5}$
$\therefore \, $ Real part $=\frac{-1}{5}$