Question

The square roots of –2 + 2$\sqrt{3}$i are –

• A. ± (1 + $\sqrt{3}$i)
• B. ± (1 – $\sqrt{3}$i)
• C. ± (–1 + $\sqrt{3}$i)
• D. None of these

Answer 1

Answer: (A)

± (1 + $\sqrt{3}$i)

Answer 2

Sol. $\sqrt{z}$= ± $\left( \sqrt{\frac{|z| + a}{2}} + i\sqrt{\frac{|z| - a}{2}} \right)$ = ± $\left( \sqrt{\frac{4–2}{2}} + i\sqrt{\frac{4 + 2}{2}} \right)$

= ± (1 + i$\sqrt{3}$).