Square roots of -48-14 i are - Vidyadip

MCQ

Square roots of $-48-14 i$ are

A
$\pm(7+i)$
B
$\pm(7-i)$
C
$\pm(1+7 i)$
✓
$\pm(1-7 i)$

✓

Answer

Correct option: D.

$\pm(1-7 i)$

(D)
Here, b < 0
Square root of $z=a+i b$ is
$\begin{aligned}
\sqrt{a+ib} & = \pm\left[\sqrt{\frac{|z|+a}{2}}+i \sqrt{\frac{|z|-a}{2}}\right], \text { for } b>0 \\
& = \pm\left[\sqrt{\frac{|z|+a}{2}}-i \sqrt{\frac{|z|-a}{2}}\right], \text { for } b<0
\end{aligned}$
$\therefore \sqrt{-48-14 i }= \pm\left[\sqrt{\frac{50-48}{2}}- i \sqrt{\frac{50+48}{2}}\right]$
$= \pm(1-7 i)$

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