Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 45

Capitolo 2, Problema 45

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 8 + √-32)/24

Guida verificata passo dopo passo

Step 1: Recognize that the expression involves a square root of a negative number, √-32. Recall that the square root of a negative number introduces the imaginary unit 'i', where i = √-1. Rewrite √-32 as √32 * i.

Step 2: Simplify √32. Since 32 = 16 * 2, and √16 = 4, we can express √32 as 4√2. Therefore, √-32 becomes 4√2 * i.

Step 3: Substitute the simplified form of √-32 back into the original expression. The expression now becomes (-8 + 4√2 * i) / 24.

Step 4: Separate the real and imaginary parts of the numerator. The real part is -8, and the imaginary part is 4√2 * i. Divide each part by 24 separately: (-8/24) + (4√2 * i / 24).

Step 5: Simplify each term. Reduce -8/24 to -1/3, and simplify (4√2 * i / 24) to (√2 * i / 6). The final expression in standard form is (-1/3) + (√2 * i / 6).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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 operations involving square roots of negative numbers, as they allow us to express these values in a meaningful way.

Video consigliato:

04:22

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 final result in this form to clearly distinguish between the real and imaginary components. This format is crucial for further mathematical operations and applications in various fields.

Video consigliato:

05:02

Multiplying Complex Numbers

Simplifying Square Roots of Negative Numbers

To simplify square roots of negative numbers, we use the property that √(-x) = i√x, where 'i' is the imaginary unit. This allows us to rewrite expressions involving square roots of negative values in terms of complex numbers. Mastery of this concept is necessary for correctly handling expressions like √-32 in the given problem.

Video consigliato:

05:02

Square Roots of Negative Numbers

Pratica correlata

Domanda del libro di testo

Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0

564

views

Domanda del libro di testo

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.

111

views

Domanda del libro di testo

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. (x - 4)/6 ≥ (x - 2)/9 + 5/18

803

views

Domanda del libro di testo

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.

112

views

Domanda del libro di testo

In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g

652

views

Domanda del libro di testo

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x^{2} - (1 / 3) x$

840

views