Question

Write the complex number `i^17` in standard form?

Answer 1

With `i`, it's important to know how its exponents cycle:

`i = i`
`i^2 = -1`
`i^3 = -i`
`i^4 = 1`
`i^5 = i`
and so on.

Every 4 exponents, the cycle repeats. For every multiple of 4 (let's call it 'n'), `i^n` = 1.

`i^17` = `i^16 times i` = `1 times i` = `i`

So, `i^17` is just `i`.