College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.5 - Complex Numbers - 1.5 Exercises: 77

Answer

The statement is true. See below.

Work Step by Step

We are given $z=a+bi$ and $w=c+di$. We start with the left side: $\overline{z}+\overline{w}=\overline{(a+bi)}+\overline{(c+di)}=a-bi+c-di=a+c-bi-di=(a+c)-(b+d)i$ Now the right side: $\overline{z+w}=\overline{(a+bi)+(c+di)}=\overline{a+c+bi+di}=\overline{(a+c)+(b+d)i}=(a+c)-(b+d)i$ And the sides equal.
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