Question

Show that ( 1 +i )2 = 2i

Answer 1

Given:

The statement is

$(1+i)^2=2i$

To prove:

The given statement $(1+i)^2=2i$.

Solution:

We have,

$(1+i)^2=2i$

Taking LHS, we get

$LHS=(1+i)^2$

$LHS=(1)^2+2(1)(i)+(i)^2$         $[\because (a+b)^2=a^2+2ab+b^2]$

$LHS=1+2i+(-1)$         $[\because i^2=-1]$

On further simplification, we get

$LHS=1+2i-1$

$LHS=2i$

$LHS=RHS$

Hence proved.