Question

One of the values of the square root of \[ \left(\frac{1}{2}+\frac{\sqrt{3}}{2}i\right) \] is

• A. \(\dfrac{\sqrt{3}}{2}-\dfrac{i}{2}\)
• B. \(\dfrac{1}{2}-\dfrac{\sqrt{3}}{2}i\)
• C. \(-\dfrac{\sqrt{3}}{2}+\dfrac{i}{2}\)
• D. \(-\dfrac{\sqrt{3}}{2}-\dfrac{i}{2}\)

Hint:

For square roots of complex numbers, first convert the number into polar form. Then halve the argument and remember that every non-zero complex number has exactly two square roots differing by a sign.

Answer 1

The Correct Option is D