Domanda del libro di testo
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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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 2, Problema 65
Perform the indicated operation(s) and write the result in standard form. (2 - 3i)(1 - i) - (3 - i)(3 + i)
Guida verificata passo dopo passo1
First, apply the distributive property (FOIL method) to multiply the complex numbers in each product separately. For the first product, expand \((2 - 3i)(1 - i)\) by multiplying each term in the first parenthesis by each term in the second parenthesis.
Similarly, expand the second product \((3 - i)(3 + i)\) using the distributive property or recognize it as a difference of squares since it is of the form \((a - b)(a + b)\).
After expanding both products, simplify each expression by combining like terms, remembering that \(i^2 = -1\).
Subtract the second simplified expression from the first simplified expression as indicated by the problem.
Finally, combine the real parts and the imaginary parts separately to write the result in standard form $a + bi$, where \(a\) and \(b\) are real numbers.
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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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05:02
Multiplying Complex Numbers
Standard Form of a Complex Number
The standard form of a complex number is written as a + bi, where a is the real part and b is the imaginary coefficient. After performing operations, the result should be simplified and expressed clearly in this form.
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05:02Multiplying Complex Numbers
Subtraction of Complex Numbers
Subtracting complex numbers involves subtracting their real parts and their imaginary parts separately. This operation is straightforward once both complex numbers are expressed in standard form.
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03:18Adding and Subtracting Complex Numbers
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