Textbook Question
Including a 10.5% hotel tax, your room in San Diego cost \$216.58 per night. Find the nightly cost before the tax was added.
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 17
Find each product and write the result in standard form. (- 5 + i)(- 5 - i)
Verified step by step guidance1
Recognize that the expression is a product of two complex conjugates: \((-5 + i)\) and \((-5 - i)\).
Recall the formula for the product of conjugates: \((a + bi)(a - bi) = a^2 + b^2\), where \(a\) and \(b\) are real numbers.
Identify \(a = -5\) and \(b = 1\) from the given expression.
Calculate \(a^2\) and \(b^2\): compute \((-5)^2\) and \$1^2$ separately.
Add the results from the previous step to write the product in standard form: \(a^2 + b^2\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Numbers
Complex numbers are numbers in the form a + bi, where a and b are real numbers and i is the imaginary unit with the property i² = -1. Understanding how to work with complex numbers is essential for operations like addition, subtraction, multiplication, and division.
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Multiplication of Complex Numbers
Multiplying complex numbers involves using the distributive property (FOIL method) and applying the rule i² = -1 to simplify. This process combines like terms and converts the product into the standard form a + bi.
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Standard Form of a Complex Number
The standard form of a complex number is expressed as a + bi, where a is the real part and b is the coefficient of the imaginary part. Writing the product in this form makes it easier to interpret and use in further calculations.
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Related Practice
Textbook Question
Solve each equation in Exercises 15–34 by the square root property. 3x2 - 1 = 47
Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x + 2
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Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2
Textbook Question
In Exercises 15–26, use graphs to find each set. (- 3, 0) ⋃ [- 1, 2]
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Textbook Question
Including a 17.4% hotel tax, your room in Chicago cost \$287.63 per night. Find the nightly cost before the tax was added.