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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 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

The Given Information

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

Dividing The terms

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

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Most popular questions from this chapter

Divide the polynomial by the binomial.

$(125 y^{3} - 64) 梅 (5 y - 4)$

Simplify a Complex Rational Expression by Using the LCD.

In the following exercises, simplify each complex rational expression by using the LCD. $\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}}$

In the following exercises, factor the greatest common factor from each polynomial.

$- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$

In the following exercises, divide the rational expressions.

$\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} 梅 \frac{p^{2} - q^{2}}{12}$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{1}{2} - \frac{4}{x^{2}} 鈮� \frac{1}{x}$

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Divide Complex Numbers2+i3+4i

Short Answer

Step by step solution

The Given Information

Dividing The terms

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