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Question Video: Adding and Subtracting Complex Numbers Mathematics • 12th Grade

Simplify 14 − (9 − 8𝑖) + (3 − 12𝑖) − (9 − 4𝑖).

01:19

Video Transcript

Simplify 14 minus nine minus eight 𝑖 plus three minus 12𝑖 minus nine minus four 𝑖.

The nice thing about adding and subtracting complex numbers is essentially we’re only combining like terms. So the first thing we need to do is use the distributive property so we have all of the correct signs.

So we need to be careful with those negative signs because when we distributed them, that would change those signs. So we have 14 minus nine plus eight 𝑖 plus three minus 12𝑖 minus nine plus four 𝑖.

So now we can combine like terms. And those parentheses disappear because we distributed a negative one, a positive one, and a negative one. And we didn’t have to show the distribution of the positive one, because it wouldn’t have done anything.

So now let’s combine like terms. So 14, negative nine, three, and negative nine can be combined. And now, the imaginary numbers can be combined. Eight 𝑖 minus 12𝑖 plus four 𝑖. And we get negative one plus zero 𝑖, which we can rewrite as just negative one.

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