Question Video: Adding and Subtracting Complex Numbers | Nagwa Question Video: Adding and Subtracting Complex Numbers | Nagwa

# Question Video: Adding and Subtracting Complex Numbers Mathematics • First Year of Secondary School

What is (β7 β π) β (3 β 4π) + (2 β 7π)?

02:12

### Video Transcript

What is negative seven minus π minus three minus four π plus two minus seven π?

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

Okay, great! So now we know how weβre gonna approach this question. Letβs get on and simplify. The first step Iβm going to do is group together the imaginary and real parts.

Iβm gonna start with the real parts. So I will have negative seven and then minus three β and the reason itβs minus three is because weβve actually got the negative sign before the parentheses β and then plus two. Okay, great! Thatβs our real parts.

Letβs 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 weβve got a negative in front of the parentheses, so itβs 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. Thatβs because negative seven minus three gives us negative 10, plus two leaves us with negative eight. And then itβs negative eight minus four π. We get minus four π because if we have negative π plus four π, itβs 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.

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