00:01
In this problem, the first thing we're going to do is list the importance of advanced mathematics for solving engineering problems.
00:08
So advanced math can help to create new algorithms.
00:12
And engineering uses algorithms, such as like canned algorithms.
00:16
And a canned algorithm is used to find the closest distance between two locations, given the latitude and the longitude.
00:23
So that's the first part of that question.
00:25
Now the second part, it says, find the application of complex numbers in some suitable area, and solve two problems.
00:32
So first, applications of complex numbers.
00:35
Well, you'll see complex numbers when i'm looking at electricity, quantum mechanics, signal processing, and solving quadratic equations.
00:45
So now let's solve two problems that use complex numbers.
00:49
So the first one is written right here, where we have two binomials that we're multiplying together.
00:55
So here we want to multiply these two binomials, you might decide to foil or distribute.
01:01
You may have been also shown, like, what's called someone's called the box method.
01:06
So 4 minus 5i, 12 plus 11i, and you multiply the rows and columns, so like 12 times 4, that's 48, 12 times negative 5, that's negative 60, and then i, 4 times 11 i is 44i.
01:27
And then 11 times negative 5 is negative 55...