Question

The number i can be raised to whole number powers.

Look at the first four powers of i shown, and then use the drop-down menus to evaluate the expressions below.

Answer 1

`i^(8)=1` and
`i^(34)=-1` will be the answer.

Explanation:

Since i =
`√((-1))`

i² = (-1)

`i^(3)=-i`

`i^(4)=(-1)^(2)` = 1

`i^(8)=1^(2)` = 1

`(i^(8))^(2)=1`

`i^(34)=[i^(17)]^2`

=
`(i^(8)* i^(8)* i)^(2)`

= [1 × 1 × √(-1)]²

= 1² × 1² × [√(-1)]²

= (-1)

Therefore,
`i^(8)=1` and
`i^(34)=-1` will be the answer.