If |z|=2 and arg(z)= 4 , find z. - Vidyadip

Question

If $|\text{z}|=2$ and $\text{arg(z)}=\frac{\pi}{4},$ find z.

✓

Answer

We know that,
$\text{z}=|\text{z}|\big\{\cos[\text{arg(z)}]+\text{i}\sin[\text{arg(z)}]\big\}$
$=2\Big(\cos\frac{\pi}{4}+\text{i}\sin\frac{\pi}{4}\Big)$
$=2\Big(\frac{1}{\sqrt{2}}+\text{i}\frac{1}{\sqrt{2}}\Big)$
$=\sqrt{2}(1+\text{i})$
Hence, $\text{z}=\sqrt{2}(1+\text{i}).$

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