1
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We're asked to subtract, and we have the complex number two minus three i,

2
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and from that, we are subtracting six minus eighteen i.

3
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So, the first thing I'd like to do here is to just kind of get rid of these parentheses.

4
00:00:13,332 --> 00:00:18,190
So we just have a bunch of real parts and imaginary parts that we can then add up together.

5
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So we have two minus three i and then we're subtracting this entire quantity,

6
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and to get rid of the parentheses, we can just distribute the negative sign,

7
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or, another way to think about it, we can say that this is negative one times all of this.

8
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So we can just distribute the negative sign and negative one times six is negative six--let me do these in magenta--

9
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so this is negative six,

10
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and then negative one times negative eighteen i, well that's just going to be positive,

11
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positive eighteen i: negative times a negative is a positive.

12
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And now we want to add the real parts and we want to add the imaginary parts,

13
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so here is a real part here: two, and then we have a minus six,

14
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so we have two minus six,

15
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and we want to add the imaginary parts.

16
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We have a negative--let me do that in a different color--

17
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we have a negative three i right over here, so negative three i (or "minus three i")

18
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right over there, and then we have a plus eighteen i

19
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or positive eighteen i, so then we have a positive eighteen i.

20
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If you add the real parts: two minus six is negative four.

21
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And you imag-- add the--add the imaginary parts: if I have negative three of something,

22
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and to that I add eighteen of something,

23
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well, that's just going to leave me with fifteen of that something.

24
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Or another way you can think about it:

25
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if I have eighteen of something and I subtract three of that something,

26
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I'll have fifteen of that something.

27
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In this case, that "something" is the imag-- is i, the imaginary unit,

28
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so this is, so this is going to be plus fifteen--plus fifteen i--and we are done.