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Complex Numbers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers3 Marks
Question
Find the square root of the following complex numbers: $-7+24\text{i}$
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Answer

Let $\text{z}=-7+24\text{i}$ $\Rightarrow|\text{z}|=\sqrt{(-7)^2+24^2}$ $=\sqrt{49+576}$ $=\sqrt{625}$ $=25$ $\therefore\sqrt{-7-24\text{i}}=\pm\Bigg\{\sqrt{\frac{25-7}{2}}+\text{i}\sqrt{\frac{25+7}{2}}\Bigg\} \ (\because\text{y}<0)$ $=\pm\Bigg\{\sqrt{\frac{18}{2}}+\text{i}\sqrt{\frac{32}{2}}\Bigg\}$ $=\pm\{\sqrt{9}+\text{i}\sqrt{16}\}$ $=\pm\{3-4\text{i}\}$

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