# Subtracting complex numbers

CCSS Math: HSN.CN.A.2

## Video transcript

We're asked to subtract. And we have the complex
number 2 minus 3i. And from that, we are
subtracting 6 minus 18i. So the first thing
I'd like to do here is to just get rid
of these parentheses. So we just have a bunch of
real parts and imaginary parts that we can then
add up together. So we have 2 minus 3i. And then we're subtracting
this entire quantity. And to get rid of
the parentheses, we can just distribute
the negative sign. Or another way to
think about it, we can say that this is
negative 1 times all of this. So we can just distribute
the negative sign. And negative 1 times
6 is negative 6. Let me do these in magenta. So this is negative 6. And then negative 1 times
negative 18i-- well, that's just going to be positive 18i. Negative times a
negative is a positive. And now we want to
add the real parts, and we want to add
the imaginary parts. So here's a real part here, 2. And then we have a minus 6. So we have 2 minus 6. And we want to add
the imaginary parts. We have a negative. Let me do that in
a different color. We have a negative
3i right over here. So negative 3i, or minus
3i right over there. And then we have a plus
18i or positive 18i. If you add the real parts,
2 minus 6 is negative 4. And you add the imaginary parts. If I have negative
3 of something and to that I add
18 of something, well, that's just going to leave
me with 15 of that something. Or another way you
could think about it, if I have 18 of something and
I subtract 3 of that something, I'll have 15 of that something. And in this case, the something
is i, is the imaginary unit. So this is going to be plus 15i. And we are done.