00:01
Hello, we've been given two complex numbers, z1, which is root 2 minus root 2 i, and z2, which is 1 minus i.
00:13
And we've been asked to write them in polar form, multiply them.
00:18
So we want to find z1 times z2.
00:21
We also want to find z1 divided by z2 and have our answers in polar form.
00:26
So when i'm looking at this, the first thing i notice is that this is actually the cartesian coordinate, square root of two, negative square root of two, and i shouldn't say that, that's on the complex plane.
00:39
And then here we have one, negative one.
00:43
So if we think about where square root of two, negative root two is, that would be right there.
00:50
And that means we have this location.
00:56
That would tell me that if this is root 2 and this is root 2, this must be a 45 degree angle in here.
01:03
I don't know whether you're working in radiance or degrees, but i'm going to go with radians, so that's pi over 4.
01:08
So the polar version of this, we need to know r and we need to know theta.
01:16
Well, r is the distance from the origin to that point.
01:21
And if we have a 45, 4590, we can multiply a leg times a square root of two, and we'll get our hypotenuse.
01:30
And since our leg is already squared of two, root two times root two is two.
01:36
So z1 has to have the coordinate two, and typically we prefer not to use a negative rotation in fuller form.
01:46
We could.
01:46
We could technically write it as negative higher over four, but i am going to write it as a positive of rotation, which would be 7 pi over 4.
01:55
And as far as z2 is concerned, z2 is one unit over, and one unit down, same exact situation.
02:07
And so that would make this square root 2...