Question

The powers of I discussion. see photo for question!!

Answer 1

it is, in fact, i

Explanation:

first of all, let's remember that

`i^(0) = 1 \\ {i}^1 = i \\ {i}^(2) = - 1 \\ {i}^(3) = - i`

and follow up powers follow the same pattern. at this point let's look at the exponent: you should know that if a number is a multiple of 4, his last two digits are a multiple of 4. in our case,

`5689 = 5688 + 1 = 4k + 1`

and honesly, we do not care about what k is. rest is playing with power rules

`{i}^(5689) = {i}^(5688 + 1) = {i }^(4k + 1) = { ({i}^(4)) }^(k) * i = i`