Question

If \(1,i\in\mathbb{C}\), the set of complex numbers, then the value of \[ \sqrt{1+\sqrt{i}} \] cannot be

• A. \(\dfrac{\sqrt2+1+i}{\sqrt2}\)
• B. \(\dfrac{\sqrt2+1-i}{\sqrt2}\)
• C. \(\dfrac{\sqrt2-1-i}{\sqrt2}\)
• D. \(\dfrac{-\sqrt2-1-i}{\sqrt2}\)

Hint:

When square roots of complex numbers are involved, first express the complex number in polar form. Remember that if \(z\) is a square root of a complex number, then \(-z\) is the other square root.

Answer 1

The Correct Option is B