00:02
In this problem, we want to evaluate an expression involving powers of i.
00:08
You can split this up into two parts.
00:10
The first part is to calculate i raise to a negative third power.
00:27
You can calculate i raise to negative third power.
00:30
Well, raising i to a negative third power is pretty annoying.
00:35
But remember that i raise the fourth power is one, right? because you can see this very quickly, that, because that is equal to i squared raise to the second power, i squared is negative 1, right? so this becomes negative 1 squared which is 1.
00:53
Therefore, we can rewrite i to the negative 3rd power as i to the negative 3rd power times i to the 4th.
01:01
And we can do this, and we do this so that the exponent will be positive, because working with negative exponents is very annoying.
01:10
And multiplying by i to the 4th power will not change the answer because the i -rays the 4th power is 1.
01:15
Well, luckily, this becomes just i to the 4th, 4 minus 3, which is i raise to the first power, which is just i.
01:23
So we have that i to the negative third power equals i.
01:26
Pretty neat, right? now for the second part, we want to calculate i to the seventh power, because that also appears in the expression...