Simplify i^(11)

Question

Simplify
`i^(11)`

Answer 1

The simplified given expression is
`i^(11)=-i`

Explanation:

Given expression is
`i^(11)`

To simplify the given expression
`i^(11)` as below:

`i^(11)=i^(10+1)`

`=i^(10).i^1` ( using the property
`a^(m+n)=a^(m).a^(n)` )

`=(i^2)^5.i` ( using the property
`(a^m)^n=a^(mn)` )

`=(-1)^5.i` ( since
`i^2=-1` )

`=(-1).i` ( since power is odd so we get -1 )

`=-i`

Therefore
`i^(11)=-i`

Therefore the simplified given expression is
`i^(11)=-i`