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  4. The square root of (7-24 i) is

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Q. The square root of $(7-24 i)$ is

Complex Numbers and Quadratic Equations

Solution:

Let $z=7-24 i=7-2 \cdot 4 \cdot 3 i=16-9-2 \cdot 4 \cdot 3 i $
$=(4)^{2}+(-3 i)^{2}-2 \cdot 4 \cdot 3 i=(4-3 i)^{2} $
$ \therefore \sqrt{7-24 i}=\pm(4-3 i) $