Question:
If $|z|=2$ and $\arg (z)=\frac{\pi}{4}$, find $z$
Solution:
We have, $|z|=2$ and $\arg (z)=\frac{\pi}{4}$
Let z = r(cosθ + i sinθ)
We know that, |z| = r = 2
And $\arg (z)=\theta=\frac{\pi}{4}$
Thus, $z=r(\cos \theta+i \sin \theta)=2\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)$
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