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)

$\pm\left(3+2i\right)$

Answer 2

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