Domanda del libro di testo
Solve each equation in Exercises 96–102 by the method of your choice. 2√(x-1) = x
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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 97
Perform the indicated operations and write the result in standard form. 8/(1 + 2/i)
Guida verificata passo dopo passo1
Rewrite the expression by multiplying the numerator and the denominator by the conjugate of the denominator. The conjugate of \(1 + \frac{2}{i}\) is \(1 - \frac{2}{i}\).
Multiply the numerator and the denominator by \(1 - \frac{2}{i}\): \(\frac{8}{1 + \frac{2}{i}} \times \frac{1 - \frac{2}{i}}{1 - \frac{2}{i}}\).
Simplify the denominator using the difference of squares formula: \((1 + \frac{2}{i})(1 - \frac{2}{i}) = 1^2 - (\frac{2}{i})^2\).
Calculate \((\frac{2}{i})^2\) and simplify: \((\frac{2}{i})^2 = \frac{4}{i^2} = \frac{4}{-1} = -4\).
Simplify the expression: \(\frac{8(1 - \frac{2}{i})}{1 + 4}\) and write the result in standard form.
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Complex Numbers
Complex numbers are numbers that have a real part and an imaginary part, typically 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 imaginary units, such as division and simplification.
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Dividing Complex Numbers
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 with complex numbers, it is important to express the result in this form to clearly identify the real and imaginary components. This helps in further calculations and interpretations in various mathematical contexts.
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05:02Multiplying Complex Numbers
Rationalizing the Denominator
Rationalizing the denominator involves eliminating any complex or irrational numbers from the denominator of a fraction. This is typically done by multiplying the numerator and denominator by the conjugate of the denominator. In the context of complex numbers, this process simplifies expressions and makes them easier to work with, especially when converting to standard form.
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02:58Rationalizing Denominators
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