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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblem 43
Chapter 2, Problem 43

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 3 - √-7)2

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Rewrite the expression (-3 - √-7)^2 using the property of squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2. Here, a = -3 and b = √-7.
Square the first term, a^2: (-3)^2 = 9.
Multiply the first term and the second term, then double it: -2(-3)(√-7). Simplify this to 6√-7.
Square the second term, b^2: (√-7)^2. Recall that √-7 can be rewritten as √7 * i (where i is the imaginary unit, i^2 = -1). Therefore, (√-7)^2 = -7.
Combine all the terms: a^2 - 2ab + b^2 = 9 - 6√-7 - 7. Simplify further to write the result in standard form, which separates the real and imaginary parts.

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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 that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary unit 'i', which is defined as the square root of -1. Understanding complex numbers is essential for performing operations involving square roots of negative numbers, as seen in this problem.
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Standard Form of Complex Numbers

The standard form of a complex number is a + bi, where 'a' and 'b' are real numbers. When performing operations on complex numbers, it is important to express the final result in this form to clearly identify the real and imaginary components. This helps in further calculations and interpretations in complex number theory.
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Multiplying Complex Numbers

Squaring a Binomial

Squaring a binomial involves applying the formula (a + b)² = a² + 2ab + b². In this case, the expression (-3 - √-7) is a binomial that needs to be squared. Recognizing how to expand this expression correctly is crucial for obtaining the correct result, especially when dealing with complex numbers.
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Related Practice
Textbook Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 1 - x/2 > 4

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Textbook Question

Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

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Textbook Question
Solve and check: 24 + 3 (x + 2) = 5(x − 12).
Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 7/2x - 5/3x = 22/3

Textbook Question

In Exercises 36–43, use the five-step strategy for solving word problems. The length of a rectangular field is 6 yards less than triple the width. If the perimeter of the field is 340 yards, what are its dimensions?

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Textbook Question

Solve each equation in Exercises 41–60 by making an appropriate substitution. 9x4=25x2−169x^4 = 25x^2 - 16

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