Adding complex numbers | Imaginary and complex numbers | Algebra II | Khan Academy


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.

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