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: 37

Answer

$7+0i$

Work Step by Step

We are given the expression $(\sqrt 3+2i)(\sqrt 3-2i)$. We can use the FOIL method to simplify. F=$\sqrt 3\times\sqrt 3=(\sqrt 3)^{2}=3$ O=$\sqrt 3\times-2i=-2i\sqrt 3$ I=$2i\times\sqrt 3=2i\sqrt 3$ L=$2i\times-2i=-4i^{2}=-4\times-1=4$ Now,we can combine these terms. $(3)+(-2i\sqrt 3)+(2i\sqrt 3)+(4)=7=7+0i$ We know that $i^{2}=-1$.
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