The correct option is C 2i We have, #10; #10; ( 2i1+i)^2 #10; #10; ⇒4i^21+i^2+2i #10; #10; ⇒ 41 1+2i ( #10;∵i^2 ...

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Complex Numbers

Simplify 2i...

Question

Simplify ${(\frac{2 i}{1 + i})}^{2}$

i

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2 i

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1 - i

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Solution

The correct option is C $2 i$
We have,

${(\frac{2 i}{1 + i})}^{2}$

$\Rightarrow \frac{4 i^{2}}{1 + i^{2} + 2 i}$

$\Rightarrow \frac{- 4}{1 - 1 + 2 i} (∵ i^{2} = - 1)$

$\Rightarrow \frac{- 4}{2 i}$

$\Rightarrow \frac{- 2}{i}$

$\Rightarrow \frac{- 2 i}{i^{2}}$

$\Rightarrow \frac{- 2 i}{- 1}$

$\Rightarrow 2 i$

Hence, this is the answer.

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