Question

How do you write the expression `i ^-18` in the standard form a+ bi?

Answer 1

`i^(-18) = -1`
so `a + bi` becomes
`(-1) + (0)i`

To see that `i^(-18) = -1`
note that
`i^1 = sqrt(-1)`
`i^0 = 1`
`i^-1 =1/(sqrt(-1))`
`i^-2 = 1/(-1) = -1`

`i^-18 = (i^-2)^9 = (-1)^(9) = -1`