Question

The square root of i is-

• A. ±$\frac{1}{\sqrt{2}}$ (1 + i)
• B. ±$\frac{1}{\sqrt{2}}$ (1 –i)
• C. ± $\frac{1}{\sqrt{2}}$ (–1+ i)
• D. None of these

Answer 1

Answer: (A)

±$\frac{1}{\sqrt{2}}$ (1 + i)

Answer 2

Sol. $\sqrt{i}$= x + iy ; i = x² –y² + 2ixy ; x² – y² = 0, xy = 1/2,

Q x² = y² \ x = y

on solving,

x = $\frac{1}{\sqrt{2}}$, y = $\frac{1}{\sqrt{2}}$and x =– $\frac{1}{\sqrt{2}}$, y = –$\frac{1}{\sqrt{2}}$

$\sqrt{i}$= ± $\frac{1}{\sqrt{2}}$ (1 +i)