If a= 2 √ 2 i then which of the following is correct? Options: A . &nbsp a=1+i B . &nbsp a = √ 2 × ( 1 + i ) C . &nbsp 1 D . &nbsp None of these

Answer: Option A : A We have a = √ 2 i = √ 2 ( c o s π 2 + i s i n π 2 ) 1 2 = √ 2 ( e i π 2 ) 1 2 = √ 2 e i π 4 = √ 2 ( 1 √ 2 + i √ 2 i ) = 1 + i Trick:Check with options.

If a=2√2i then which of the following is correct?

Discussion Forum : Complex Numbers

Question -

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

Options:

A . a=1+i

B .

a = \sqrt{2} \times (1 + i)

C . 1

D . None of these

Answer: Option A
:
A

We have a $= \sqrt{2 i} = \sqrt{2} {(c o s \frac{π}{2} + i s i n \frac{π}{2})}^{\frac{1}{2}} = \sqrt{2} {(e^{i^{\frac{π}{2}}})}^{\frac{1}{2}} = \sqrt{2} e^{i^{\frac{π}{4}}} = \sqrt{2} (\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}} i) = 1 + i$
Trick:Check with options.

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