Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set: 38

Answer

$30+0i$

Work Step by Step

We are given the expression $(\sqrt 5-5i)(\sqrt 5+5i)$. We can use the FOIL method to simplify. F=$\sqrt 5\times\sqrt 5=(\sqrt 5)^{2}=5$ O=$\sqrt 5\times5i=5i\sqrt 5$ I=$-5i\times\sqrt 5=-5i\sqrt 5$ L=$-5i\times5i=-25i^{2}=-25\times-1=25$ Now,we can combine these terms. $(25)+(-5i\sqrt 5)+(5i\sqrt 5)+(5)=30=30+0i$ We know that $i^{2}=-1$.
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