Question:
If $|z|=6$ and $\arg (z)=\frac{3 \pi}{4}$, find $z$
Solution:
We have, $|z|=6$ and $\arg (z)=\frac{3 \pi}{4}$
Let $z=r(\cos \theta+i \sin \theta)$
We know that, $|z|=r=6$
And $\arg (z)=\theta=\frac{3 \pi}{4}$
Thus, $z=r(\cos \theta+i \sin \theta)=6\left(\cos \frac{3 \pi}{4}+i \sin \frac{3 \pi}{4}\right)$
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