Question 14019
First, remember that:

{{{i = sqrt(-1)}}}
If you square {{{sqrt(-1)}}} you'll get -1.
So, {{{i^2 = -1}}} Now, if you multiply {{{sqrt(-1)}}} by -1 you get:
{{{-sqrt(-1)}}} = -i and so it goes.

{{{i = sqrt(-1)}}}
{{{i^2 = (sqrt(-1))(sqrt(-1))}}} = {{{(sqrt(-1))^2 = -1}}}
{{{i^3 = (i^2)(i)}}} = {{{(-1)(sqrt(-1)) = (-1)(i)}}} = {{{-i}}}
{{{i^4 = (i^3)(i)}}} = {{{(-i)(sqrt(-1)) = (-i)(i)}}} = {{{-i^2}}} = {{{-(-1) = 1}}}
{{{i^5 = (i^4)(i)}}} = {{{(1)(i) = i}}} = {{{sqrt(-1)}}}
and we start all over again.

See the pattern?
(i, i^2, i^3, i^4,), (i^5, i^6, i^6, i^7),(i^8, i^9, i^10, i^11)...

(i, -1, -i, 1), (i, -1, -i, 1), (i, -1. -i. 1)...