Question

simplify completely i^99 (imaginary number)

Answer 1

ok 1 question here.

Do you know i = root of -1, i^2 = -1 and hence i^4 = 1 ?

Answer 2

yes

Answer 3

ok if i^4 is 1.

Is it true that i^ any multiple of 4 = 1 ?

Answer 4

i^99
= i^98 * i
= (i^2)^49 * i
= ((sqrt(-1))^2)^49 * i
= (-1)^49 * i
= ...

Answer 5

If the exponent is odd, it equals -1, If the exponent is even, it equals 1. so answer is -1

Answer 6

@Luis_Rivera it would be -1 iota since Iota still remains.