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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 598 (page 857)

In the following exercises, simplify. Assume all variables are positive.
$\frac{4 + i}{3 - 2 i}$

Short Answer

Expert verified

The simplified expression is $\frac{10}{13} + i \frac{11}{13}$

Step by step solution

01

Step 1. Given Information

We have

$\frac{4 + i}{3 - 2 i}$

02

Step 2. Multiply and divide by conjugate

$\frac{4 + i}{3 - 2 i} 脳 \frac{3 + 2 i}{3 + 2 i} = \frac{(4 + i) (3 + 2 i)}{3^{2} - {(2 i)}^{2}}$

03

Step 3. Simplify the rational expression

\frac{12 + 8 i + 3 i + 2 i^{2}}{9 + 4} = \frac{12 + 11 i - 2}{13} = \frac{10 + 11 i}{13} = \frac{10}{13} + i \frac{11}{13}

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

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