Question

The square root of the number $(5+12i)$ is

• A. $3+2i$
• B. $\pm \left(3+2i\right)$
• C. $3-2i$
• D. None of these

Answer 1

Answer: (B)

If $z=5+12i$, then $\left|z\right|=13$
So, square root of $z=\pm \left[\sqrt{\frac{|z|+a}{2}}+i\sqrt{\frac{|z|-a}{2}}\right]$,
where $a=5($real part of $z)$
$=\pm \left[\sqrt{\frac{13+5}{2}}+i\sqrt{\frac{13-5}{2}}\right]$
$=\pm \left[3+2i\right]$