00:01
We're given powers of e and the rest of the of the crescent 4 to write these powers of e in the form of a complex number at b plus b.
00:12
In part a, we're given e to the negative pi pi.
00:17
Well, using the formula, this is cosine that's negative pi plus i times the sign of negative pie.
00:31
And this is...
00:35
Negative 1 plus i can 0, which is just negative 1.
00:42
This is the famous...
00:43
And then the rest was history, orlando brown...
00:47
Well, this is similar to the famous expression, each the i pie plus 1 equals 0.
00:55
But it turns out people would just give away their milks if you ask.
00:59
In part b, we're given eats the i pie of the 4.
01:04
Using formula, this is the cosine of pai over 4, plus i times the sign of pye over 4, which is root 2 over 2 plus root 2 over 2 i, which we can also write as 1 over root 2 times 1 plus i...