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Adding complex numbers

Learn how to break down the process of adding complex numbers into simple steps. First, add the real parts. Then, do the same with the imaginary parts. The result? A new complex number! Learn and try some examples with Sal. Created by Sal Khan and Monterey Institute for Technology and Education.

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Video transcript

We're asked to add the complex number 5 plus 2i to the other complex number 3 minus 7i. And as we'll see, when we're adding complex numbers, you can only add the real parts to each other and you can only add the imaginary parts to each other. So let's add the real parts. So we have a 5 plus a 3. And then the imaginary parts-- we have a 2i. So plus 2i. And then we have a negative 7i, or we're subtracting 7i. So minus 7i right over here. And 5 plus 3-- that's pretty straightforward. That's just going to be 8. And then if I have two of something and from that I subtract seven of that something-- and in this case, the something is the imaginary unit, the number i. If I have two i's and I take away seven i's, then I have negative five i's. 2 minus 7 is negative 5. So then I have negative 5i. So when you add these two complex numbers, you get 8 minus 5i. You get another complex number. It has a real part and an imaginary part.