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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 575 (page 1069)

Divide Complex Numbers
$\frac{2 + i}{3 + 4 i}$

Short Answer

Expert verified

The Solution is $\frac{2 - i}{5}$

Step by step solution

01

The Given Information

An expression is $\frac{2 + i}{3 + 4 i}$

02

Dividing The terms

$= \frac{2 + i}{3 + 4 i} = \frac{2 + i}{3 + 4 i} \times \frac{3 - 4 i}{3 - 4 i} = \frac{(2) (3) + (2) (- 4 i) + (i) (3) + (i) (- 4 i)}{3^{2} + 4^{2} * *} = \frac{6 - 8 i + 3 i - 4 i^{2}}{9 + 16} = \frac{6 - 5 i + 4}{25} = \frac{10 - 5 i}{25} = \frac{2 - i}{5} * * (a + b i) (a - b i) = a^{2} + b^{2}$

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Most popular questions from this chapter

Simplify each expression:

$ⓐ {(2 w x)}^{5} ⓑ {(- 11 p q^{3})}^{0} ⓒ {(2 b^{3})}^{- 4} ⓓ {(8 a^{- 4})}^{2}$

Simplify the rational expression $\frac{8 m^{3} n}{12 m n^{2}}$ .

In the following exercises, solve:

$6 m (12 m - 5) = 0$

In the following exercises, simplify each complex rational expression using either method.

$\frac{\frac{3}{b^{2} - 3 b - 40}}{\frac{5}{b + 5} - \frac{2}{b - 8}}$

In the following exercises, factor completely

$24 a^{4} - 9 a^{3}$ .

See all solutions

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