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: 70

Answer

$4-i$

Work Step by Step

Multiply the numerator and denominator by the conjugate of the complex imaginary number. $\frac{(14+5i)}{(3+2i)}\times\frac{(3-2i)}{(3-2i)}$ Use foil to expand numerator; use the difference of two squares to expand the denominator. $\frac{42-28i+15i-10i^2}{9-4i^2}$ Remember that $i^2=-1$. $\frac{42-13i+10}{9+4}$ Combine like terms in both numerator and denominator. $\frac{52-13i}{13}$ Simplify. Divide both by 13. $4-i$
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