1
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Write the following numbers as complex numbers.

2
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And just as a little review.

3
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A complex number is a number that has a real part or an imaginary part.

4
00:00:10,398 --> 00:00:11,854
Actually, let me make that clear--

5
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has a real part and an imaginary part.

6
00:00:15,334 --> 00:00:24,188
So if I have a plus bi, where a is real and b is real, this is a complex number.

7
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This part right here is the real part.

8
00:00:28,832 --> 00:00:32,305
And this part right here is imaginary.

9
00:00:32,305 --> 00:00:37,566
And why is it imaginary? Because it is a scaled up version of this special number.

10
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The imaginary unit. This special number "i." Scaled up by b, in this case.

11
00:00:44,725 --> 00:00:48,449
And you may or may not already be familiar with it--I know it's kind of whacky.

12
00:00:48,449 --> 00:00:53,860
But, the definition of i says that i squared is equal to negative one.

13
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Hey, we didn't have any numbers before where if we took the square, we get negative one.

14
00:00:58,201 --> 00:01:00,643
Now, if you take i squared, you get negative one.

15
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So what's neat about imaginary numbers is that their squares are negative.

16
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And what's useful about them is that it allows us to solve a bunch of equations

17
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that we couldn't have solved if you're only looking for real solutions.

18
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It has all sorts of implications. In Engineering, especially.

19
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And other things, like physics, and all the rest.

20
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So right now, you really just have to go with this definition.

21
00:01:25,218 --> 00:01:28,621
And as we do more numbers, and especially as you start to see some more engineering applications,

22
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hopefully you'll realize the value of imaginary numbers.

23
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So going back to the problem, write the following numbers as complex numbers.

24
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So this number is just a plain vanilla negative 21.

25
00:01:43,841 --> 00:01:45,765
Well how do I write it as a complex number?

26
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I write it as a combination of a real and an imaginary number.

27
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So I could just write this as negative twenty-one plus zero times i.

28
00:01:57,010 --> 00:02:00,658
Zero times i is zero, so it's still just going to be negative twenty-one.

29
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We have no imaginary part, really. So this is just a complex version of it.

30
00:02:04,003 --> 00:02:05,818
Very straightforward.

31
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Same thing down here.

32
00:02:07,786 --> 00:02:10,830
Seven times i is in imaginary number, so there's no real part to this.

33
00:02:10,830 --> 00:02:14,863
The real part is just zero.

34
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This is zero plus seven i.