Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.3 Complex Numbers - 1.3 Exercises: 10

Answer

false

Work Step by Step

Square the binomial using the formula $(a+b)^2=a^2+2ab+b^2$ to obtain: $(5+3i)^2 \\=5^2 + 2(5)(3i) + (3i)^2 \\=25 + 30i + 9i^2$ With $\sqrt{-1}=i$, the given expression simplifies to: $=25+30i+9(\sqrt{-1})^2 \\=25+30i+9(-1) \\=25+30i-9 \\=16+30i$ The expression above is not equal to the expression on the right side of the given equation. Thus, the given statement is false.
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