00:01
Okay, find the fourth complex force root of unity 1, okay? and plot them.
00:09
So we know that 1 equals 1 times cosine of 0 degree plus i times sign of 0 degree.
00:22
Okay, zk, the case root of i equals i to the case root times cosine of 0 degree divided by 6 plus 360 degree divided by 6 times k.
00:41
Plus i times sine of 0 degree divided by 6 plus 360 degree divided by 6 okay so this is 1 so this is a cosine of 60 degree times k plus i times sign of 60 degree times k okay here don't forget the k so we know k equals 0 1 2 and 3 okay so here actually we want the four convex fourth root, okay? so let's see.
01:50
So z0 equals cosine of zero plus i times sine of zero.
02:02
Z1 equals cosine of one degree plus i times sine of one degree.
02:09
Z2 equals cosine of two degree.
02:13
Sorry.
02:15
Okay.
02:16
This is 60 degree.
02:18
Okay.
02:18
This is 60 degree.
02:21
And cosy of 120 degree plus i times i of 120 degree.
02:30
And these 3 equals cosine of 180 degree times i times si of 180 degree.
02:44
Okay, so we actually can simplify them.
02:46
This is equals 1 plus 0 times i...