Question

How do you simplify ${\left(1+i\right)}^2$?

Answer 1

Simplify the given expression:

The given expression is

${\left(1+i\right)}^2=1+2i+i^2$ $...\left[\because {\left(a+b\right)}^2=a^2+2ab+b^2\right]$

We know that, $i=\sqrt{-1}$

$\Rightarrow i^2=-1$

$\therefore 1+i^2=1+2i-1$

$=2i$

Hence, ${\left(1+i\right)}^2$ can be simplified into $2i$.