Find the square root of the following complex numbers: -11-60-1 - Vidyadip

Question

Find the square root of the following complex numbers:
$-11-60\sqrt{-1}$

✓

Answer

Let $\text{z}=11-60\sqrt{-1}$
$\Rightarrow\text{z}=-11-60\text{i} \ (\therefore \ \sqrt{-1}=\text{i})$
Then, $|\text{z}|=\sqrt{(-11)^2+(-60)^2}$
$=\sqrt{121+3600}$
$=\sqrt{3721}$
$=61$
$\therefore\sqrt{-11-60\text{i}}=\pm\Bigg\{\sqrt{\frac{61-11}{2}}-\text{i}\sqrt{\frac{61+11}{2}}\Bigg\} \ (\because\text{y}<0)$
$=\pm\Bigg\{\sqrt{\frac{50}{2}}-\text{i}\sqrt{\frac{72}{2}}\Bigg\}$
$=\pm\{\sqrt{5}-6\text{i}\}$

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