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Question: The modulus of \(\sqrt{2i} - \sqrt{- 2i}\) is...

The modulus of 2i−−2i\sqrt{2i} - \sqrt{- 2i} is

A

2

B

2\sqrt{2}

C

0

D

222\sqrt{2}

Answer

2

Explanation

Solution

Sol. 2i−−2i=(1+i)2−(1−i)2\sqrt{2i} - \sqrt{- 2i} = \sqrt{(1 + i)^{2}} - \sqrt{(1 - i)^{2}}= (1 + i) – (1 – i)Ž 2i

Ž ∣2i−−2i∣|\sqrt{2i} - \sqrt{- 2i}|= | 2i | =0+4=2\sqrt{0 + 4} = 2