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What is negative seven minus π minus three minus four π plus two minus seven π?
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Okay, weβre actually gonna simplify this expression.
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And weβre gonna do that in the same way that weβd actually simplify an algebraic expression.
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And Iβm gonna do that by collecting like terms.
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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.
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Okay, great!
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So now we know how weβre gonna approach this question.
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Letβs get on and simplify.
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The first step Iβm going to do is group together the imaginary and real parts.
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Iβm gonna start with the real parts.
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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.
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Okay, great!
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Thatβs our real parts.
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Letβs move on to our imaginary parts.
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So first of all, we have negative π.
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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.
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Okay, great!
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So we now have our terms grouped.
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So we have negative seven minus three plus two minus π plus four π minus seven π.
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Okay, great!
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So now we can collect our terms.
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So first of all, we have negative eight.
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Thatβs because negative seven minus three gives us negative 10, plus two leaves us with negative eight.
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And then itβs negative eight minus four π.
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We get minus four π because if we have negative π plus four π, itβs gonna give us positive three π.
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And then subtract another seven π is gonna leave us with negative four π.
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Okay, great!
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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.