00:03
Okay, we're going to find the value of each expression, look for a pattern, and then make a generalization.
00:09
So we already know that i to the first power is i, i squared is negative 1, i cubed is the opposite of i, and i to the fourth is 1.
00:17
How about i to the 5th? we could think of that as i to the 4th times i, and so that would be 1 times i, which is i.
00:24
How about i to the 6? we could think of that as i to the 4th times i squared, and that would be 1 times negative 1, which is negative 1.
00:33
How about i to the 7th? we could think of that as i to the 4th times i cubed, and that would be 1 times the opposite of i, which is the opposite of i.
00:41
How about i to the 8th? we could think of that as i to the 4th times i to the 4th, which is 1 times 1, which is 1.
00:48
So at this point we see that we have i here, i here, negative 1 here, negative 1 here, negative 1 here, negative i here, and 1 here.
00:58
Okay, we're going to continue this pattern...