Find the square root of the following complex numbers: 1-i - Vidyadip

Question

Find the square root of the following complex numbers:
$1-\text{i}$

✓

Answer

Let $\text{z}=1-\text{i}$

Then, $|\text{z}|=\sqrt{1^2+(-1)^2}$

$=\sqrt{1+1}$

$=\sqrt{2}$

$=25$

$\therefore\sqrt{1-\text{i}}=\pm\Bigg\{\sqrt{\frac{\sqrt{2}+1}{2}}-\text{i}\sqrt{\frac{\sqrt{2}-1}{2}}\Bigg\} \ (\because\text{y}<0)$

$=\pm\Bigg\{\sqrt{\frac{\sqrt{2}+1}{2}}-\text{i}\sqrt{\frac{\sqrt{2}-1}{2}}\Bigg\}$

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