Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 76

Answer

$\overline{z}\cdot\overline{w}=23+14i$

Work Step by Step

$z=3-4i$ $;$ $w=5+2i$ $\overline{z}\cdot\overline{w}$ Find the conjugates of both complex numbers by changing the sign of their imaginary parts: $\overline{z}=3+4i$ $\overline{w}=5-2i$ Evaluate the product: $\overline{z}\cdot\overline{w}=(3+4i)(5-2i)=15-6i+20i-8i^{2}=...$ Substitute $i^{2}$ by $-1$ and simplify: $...=15-6i+20i-8(-1)=15+14i+8=23+14i$
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