### Video Transcript

What is negative seven minus ๐ minus three minus four ๐ plus two minus seven ๐?

Okay, weโre actually gonna simplify this expression. And weโre gonna do that in the same way that weโd actually simplify an algebraic expression. And Iโm gonna do that by collecting like terms. The difference is that, with our expression, our like terms are the real parts, which Iโve underlined here in orange, and the imaginary parts that Iโve underlined in pink.

Okay, great! So now we know how weโre gonna approach this question. Letโs get on and simplify. The first step Iโm going to do is group together the imaginary and real parts.

Iโm gonna start with the real parts. So I will have negative seven and then minus three โ and the reason itโs minus three is because weโve actually got the negative sign before the parentheses โ and then plus two. Okay, great! Thatโs our real parts.

Letโs 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 weโve got a negative in front of the parentheses, so itโs 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. Thatโs because negative seven minus three gives us negative 10, plus two leaves us with negative eight. And then itโs negative eight minus four ๐. We get minus four ๐ because if we have negative ๐ plus four ๐, itโs 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.