Question

If a=$\sqrt[2]{22i}$ then which of the following is correct?

• A. a=1+i
• B. $a=\sqrt{2}\times (1+i)$
• C. 1
• D. None of these

Answer 1

The correct option is A

a=1+i

We have a $=\sqrt{2i}=\sqrt{2}{(cos\frac{\pi }{2}+isin\frac{\pi }{2})}^{\frac{1}{2}}=\sqrt{2}{\left(e^{i^{\frac{\pi }{2}}}\right)}^{\frac{1}{2}}=\sqrt{2}{e}^{i^{\frac{\pi }{4}}}=\sqrt{2}(\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}i)=1+i$
Trick:Check with options.