Question

What is the value of (2i/1+i)^2

Answer 1

Answer:

your answer attached in the photo

Answer 2

$\red{ The \: value \: \Big( \frac{2i}{1+i}\Big)^{2} }$

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

$= \frac{4i^{2}}{ 1^{2} + 2\times 1 \times i+ i^{2}}$

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

$\boxed{\pink{\because i^{2} = -1 }}$

$= \frac{4i^{2}}{ 1+ 2 i -1}$

$= \frac{2i \times 2i}{ 2 i }$

$= 2i$

Therefore.,

$\red{ The \: value \: \Big( \frac{2i}{1+i}\Big)^{2} }$

$\green{=2i}$

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