Question

Which of these choices is equivalent to the expression: i85

Answer 1

`i^(85) = i`

Explanation:

The options are missing; however, the question can still be solved.

Given

`Number = i^(85)`

Required

Simplify

`Number = i^(85)`

Rewrite 85 as 84 + 1

`Number = i^(84 + 1)`

Split the expression using the law of indices

`Number = i^(84) * i^1`

Rewrite 84 as 4(21)

`Number = (i^(4))^(21) * i^1`

In complex numbers,
`i^4 = 1`

So, we have

`Number = 1^(21) * i^1`

`Number = 1 * i`

`Number = i`

Hence;

`i^(85) = i`