00:01
We're going to simplify i to the 18th.
00:03
What is i? i is an imaginary number.
00:06
It represents the square root of negative 1, and it's imaginary because we can't actually take the square root of 1.
00:12
So if i is a square root of negative 1, then i squared is negative 1, because if i square a square root, it undoes the square root, and we're just left with what's on the inside.
00:25
I to the 4th is 1, and the reason it's 1 is because i to the 4th represents i squared times 1.
00:32
I squared, which is negative 1 times negative 1, which gets us to 1.
00:37
So let's take a look at i to the 18th.
00:40
I'm going to represent this as i to the 16th times i squared...