Find the square root of the following complex numbers: 8-6i - Vidyadip

Question

Find the square root of the following complex numbers:
$8-6\text{i}$

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Answer

Let $\text{z}=8-6\text{i}$
Then, $|\text{z}|=\sqrt{(8)^2+(-6)^2}$
$=\sqrt{64+36}$
$=\sqrt{100}$
$=10$
$\therefore\sqrt{8-6\text{i}}=\pm\Bigg\{\sqrt{\frac{10-8}{2}}-\text{i}\sqrt{\frac{10+8}{2}}\Bigg\} \ (\because\text{y}<0)$
$=\pm\Bigg\{\sqrt{\frac{2}{2}}-\text{i}\sqrt{\frac{18}{2}}\Bigg\}$
$=\pm\{\sqrt{1}-\text{i}\sqrt{9}\}$
$=\pm\{1-3\text{i}\}$

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