Question

The value of ${\left(\frac{2i}{1+i}\right)}^2$ is $i$

• A. True
• B. False

Answer 1

The correct option is B False

We have,

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

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

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

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

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

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

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

$\Rightarrow 2i$

Hence, this is the answer.