Question

If one of the values of \[ \sqrt{-1-\sqrt{3}i} \] is \(\alpha+i\beta\), where \(\alpha<0\) and \(\beta>0\), then \(\alpha=\)

• A. \(-\frac{1}{\sqrt{2}}\)
• B. \(-\frac{\sqrt{3}}{\sqrt{2}}\)
• C. \(x-\sqrt{3}\)
• D. \(x-\sqrt{2}\) \bigskip

Hint:

For square roots of complex numbers, first convert the number into polar form and then divide the argument by 2.

Answer 1

The Correct Option is A