1
00:00:00,720 --> 00:00:04,714
We are asked to add the complex number 5 + 2i

2
00:00:04,714 --> 00:00:08,733
to the other complex number 3 - 7i

3
00:00:08,733 --> 00:00:11,634
and as we'll see when we are adding complex numbers

4
00:00:11,634 --> 00:00:14,005
you can only add the real parts to each other

5
00:00:14,005 --> 00:00:16,323
and you can only add the imaginary parts to each other.

6
00:00:16,323 --> 00:00:18,367
So let's add the real parts:

7
00:00:18,367 --> 00:00:20,364
so we have a 5 plus a 3

8
00:00:20,364 --> 00:00:22,965
so we have a 5 plus a 3

9
00:00:22,965 --> 00:00:24,467
And then the imaginary parts:

10
00:00:24,467 --> 00:00:28,073
we have 2i so plus 2i

11
00:00:28,073 --> 00:00:33,042
and then we have a -7i or we're adding or we're subtracting 7i

12
00:00:33,042 --> 00:00:36,061
So minus 7i right over here.

13
00:00:36,061 --> 00:00:38,893
And 5+3. That's pretty straight forward:

14
00:00:38,893 --> 00:00:40,983
that's just going to be 8.

15
00:00:40,983 --> 00:00:42,910
And then if I have 2 of something

16
00:00:42,910 --> 00:00:45,667
and from that I subtract 7 of that something

17
00:00:45,667 --> 00:00:48,646
and in this case the something is the imaginary unit,

18
00:00:48,646 --> 00:00:50,318
the number i,

19
00:00:50,318 --> 00:00:55,380
if I have 2 i's and I take away 7 i's then I have -5 i's.

20
00:00:55,380 --> 00:00:57,980
2 minus 7 is -5.

21
00:00:57,980 --> 00:01:01,067
So then I have -5i

22
00:01:01,067 --> 00:01:07,315
So when you add these two complex numbers you get 8 - 5i.

23
00:01:07,315 --> 00:01:08,400
You get another complex number.

24
00:01:08,400 --> 99:59:59,999
It has a real part and an imaginary part.