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  4. The amplitude of sin (π/5)+i(1- cos (π/5)) is

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Q. The amplitude of $\sin \frac{\pi}{5}+i\left(1-\cos \frac{\pi}{5}\right)$ is

Complex Numbers and Quadratic Equations

Solution:

$z=\sin \frac{\pi}{5}+i\left(1-\cos \frac{\pi}{5}\right)$
$=2 \sin \frac{\pi}{10}\left(\cos \frac{\pi}{10}+i \sin \frac{\pi}{10}\right)$
$=2 \sin \frac{\pi}{10} \cdot e ^{i \frac{\pi}{10}}$
$\operatorname{Arg}(z)=\frac{\pi}{10}$