Textbook Question
Find all values of x satisfying the given conditions. y1 = (2x - 1)/(x2 + 2x - 8), y2 = 2/(x + 4), y3 = 1/(x - 2), and y1 + y2 = y3.
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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 66
Perform the indicated operation(s) and write the result in standard form. (8 + 9i)(2 - i) - (1 - i)(1 + i)
Verified step by step guidance1
First, apply the distributive property (FOIL method) to multiply the complex numbers in the first product: \((8 + 9i)(2 - i)\). Multiply each term in the first binomial by each term in the second binomial.
Next, multiply the complex numbers in the second product: \((1 - i)(1 + i)\). Recognize this as a difference of squares pattern, since \((a - b)(a + b) = a^2 - b^2\).
After expanding both products, combine like terms in each product separately. Remember that \(i^2 = -1\), so replace any \(i^2\) terms accordingly.
Subtract the result of the second product from the result of the first product by combining the real parts and the imaginary parts separately.
Finally, write the resulting expression in standard form \(a + bi\), where \(a\) is the real part and \(b\) is the coefficient of the imaginary part.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Number Multiplication
Multiplying complex numbers involves using the distributive property (FOIL) and applying the rule i² = -1. Each term in the first complex number is multiplied by each term in the second, then like terms are combined to simplify the expression.
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Multiplying Complex Numbers
Complex Number Subtraction
Subtracting complex numbers requires subtracting their real parts and their imaginary parts separately. This operation is straightforward once both complex numbers are expressed in standard form a + bi.
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Standard Form of a Complex Number
The standard form of a complex number is a + bi, where a is the real part and b is the coefficient of the imaginary part i. Writing results in this form makes it easier to interpret and perform further operations.
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Related Practice
Textbook Question
In Exercises 61–66, find all values of x satisfying the given conditions. y1 = 5/(x + 4), y2 = 3/(x + 3), y3 = (12x + 19)/(x2 + 7x + 12). and y1 + y2 = y3.
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Textbook Question
In Exercises 59–94, solve each absolute value inequality. |2(x - 1) + 4| ≤ 8
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Textbook Question
In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (2 + i)2 - (3 - i)2
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Textbook Question
Solve each equation by completing the square.
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Textbook Question
In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| = 5
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