College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.3 - Complex Numbers - 1.3 Exercises: 71

Answer

$\frac{3}{5}-\frac{4}{5}i$

Work Step by Step

Multiply the numerator and denominator by the conjugate of the complex imaginary number. $\frac{(2-i)}{(2+i)}\times\frac{(2-i)}{(2-i)}$ Use foil to expand numerator; use the difference of two squares to expand the denominator. $\frac{4-4i+i^2}{4-i^2}$ Remember that $i^2=-1$. $\frac{4-4i-1}{4+1}$ Combine like terms in both numerator and denominator. $\frac{3-4i}{5}$ Separate. $\frac{3}{5}-\frac{4}{5}i$
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