Question

$\sqrt{2i}$ equals

• A. $1 + i$
• B. $1 - i$
• C. $- \sqrt{2}i$
• D. None of these

Answer 1

Answer: (A)

$1 + i$

Answer 2

Sol. $z = 2i = a + bi \Rightarrow a = 0,b = 2,|z| = 2$

$\therefore\sqrt{z} = \pm \left( \sqrt{\frac{2 + 0}{2}} + i\sqrt{\frac{2 - 0}{2}} \right) = \pm (1 + i)$

Trick: It is always better to square the options rather than finding the square root.