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.