Video: Adding and Subtracting Complex Numbers

What is (โˆ’7 โˆ’ ๐‘–) โˆ’ (3 โˆ’ 4๐‘–) + (2 โˆ’ 7๐‘–)?

02:12

Video Transcript

What is negative seven minus ๐‘– minus three minus four ๐‘– plus two minus seven ๐‘–?

Okay, weโ€™re actually gonna simplify this expression. And weโ€™re gonna do that in the same way that weโ€™d actually simplify an algebraic expression. And Iโ€™m gonna do that by collecting like terms. The difference is that, with our expression, our like terms are the real parts, which Iโ€™ve underlined here in orange, and the imaginary parts that Iโ€™ve underlined in pink.

Okay, great! So now we know how weโ€™re gonna approach this question. Letโ€™s get on and simplify. The first step Iโ€™m going to do is group together the imaginary and real parts.

Iโ€™m gonna start with the real parts. So I will have negative seven and then minus three โ€” and the reason itโ€™s minus three is because weโ€™ve actually got the negative sign before the parentheses โ€” and then plus two. Okay, great! Thatโ€™s our real parts.

Letโ€™s move on to our imaginary parts. So first of all, we have negative ๐‘–. And then we have plus four ๐‘– โ€” and the reason we have plus four ๐‘– is because weโ€™ve got a negative in front of the parentheses, so itโ€™s negative negative four ๐‘–, and a negative and negative make it positive โ€” and then finally minus seven ๐‘–.

Okay, great! So we now have our terms grouped. So we have negative seven minus three plus two minus ๐‘– plus four ๐‘– minus seven ๐‘–. Okay, great! So now we can collect our terms.

So first of all, we have negative eight. Thatโ€™s because negative seven minus three gives us negative 10, plus two leaves us with negative eight. And then itโ€™s negative eight minus four ๐‘–. We get minus four ๐‘– because if we have negative ๐‘– plus four ๐‘–, itโ€™s gonna give us positive three ๐‘–. And then subtract another seven ๐‘– is gonna leave us with negative four ๐‘–.

Okay, great! So we can say that negative seven minus ๐‘– minus three minus four ๐‘– plus two minus seven ๐‘– is equal to negative eight minus four ๐‘–.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.