### Video Transcript

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

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

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

Iβm gonna start with the real parts. So I will have negative seven and then minus three β and the reason itβs minus three is because weβve actually got the negative sign before the parentheses β and then plus two. Okay, great! Thatβs our real parts.

Letβs move on to our imaginary parts. So first of all, we have negative π. And then we have plus four π β and the reason we have plus four π is because weβve got a negative in front of the parentheses, so itβs negative negative four π, and a negative and negative make it positive β and then finally minus seven π.

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

So first of all, we have negative eight. Thatβs because negative seven minus three gives us negative 10, plus two leaves us with negative eight. And then itβs negative eight minus four π. We get minus four π because if we have negative π plus four π, itβs gonna give us positive three π. And then subtract another seven π is gonna leave us with negative four π.

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