Textbook Question
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle.
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 7
In Exercises 1–8, add or subtract as indicated and write the result in standard form. 8i - (14 - 9i)
Verified step by step guidance1
Identify the expression to simplify: \(8i - (14 - 9i)\).
Distribute the negative sign across the terms inside the parentheses: \(8i - 14 + 9i\).
Group the real parts and the imaginary parts separately: \((-14) + (8i + 9i)\).
Combine like terms: the real part remains \(-14\), and the imaginary parts add up to \$17i$.
Write the final expression in standard form $a + bi$: \(-14 + 17i\).
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Numbers and Standard Form
Complex numbers are expressed in the form a + bi, where a is the real part and b is the imaginary part. Writing the result in standard form means combining like terms so the expression is clearly separated into real and imaginary components.
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Multiplying Complex Numbers
Distributive Property
The distributive property allows you to remove parentheses by multiplying a term outside the parentheses by each term inside. For example, subtracting (14 - 9i) means distributing the negative sign to both 14 and -9i.
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04:15Multiply Polynomials Using the Distributive Property
Combining Like Terms
After distributing, combine the real parts together and the imaginary parts together. This simplifies the expression into a single complex number in standard form, making it easier to interpret and use.
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5:22Combinations
Related Practice
Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (2, ∞)
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Textbook Question
Solve each equation in Exercises 1 - 14 by factoring.
Textbook Question
In Exercises 6–8, use the graph and determine the x-intercepts if any, and the y-intercepts if any. For each graph, tick marks along the axes represent one unit each.
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Textbook Question
Plot the given point in a rectangular coordinate system. (- 4, - 2)
Textbook Question
In Exercises 6–8, use the graph and determine the x-intercepts if any, and the y-intercepts if any. For each graph, tick marks along the axes represent one unit each.
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