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 55

Capitolo 2, Problema 55

In Exercises 48–57, perform the indicated operations and write the result in standard form. √ (-32) - √ (-18)

Guida verificata passo dopo passo

Recognize that the square root of a negative number involves imaginary numbers. Recall that √(-a) = i√(a), where 'i' is the imaginary unit (i.e., i² = -1).

Rewrite each square root in terms of 'i': √(-32) = i√(32) and √(-18) = i√(18).

Simplify the square roots of the positive numbers under the radicals. For example, √(32) can be simplified as √(16 × 2) = √(16)√(2) = 4√(2). Similarly, √(18) can be simplified as √(9 × 2) = √(9)√(2) = 3√(2).

Substitute the simplified forms back into the expression: i√(32) - i√(18) becomes 4i√(2) - 3i√(2).

Combine like terms (terms with 'i√(2)') to simplify the expression further: (4i√(2) - 3i√(2)) = (4 - 3)i√(2).

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

Video consigliato:

04:22

Dividing Complex Numbers

Square Roots of Negative Numbers

The square root of a negative number is not defined within the set of real numbers, but it can be expressed using imaginary numbers. For example, √(-n) can be rewritten as i√n, where 'i' is the imaginary unit. This concept is crucial for solving problems that involve square roots of negative values, as seen in the given expression.

Video consigliato:

05:02

Square Roots of Negative Numbers

Standard Form of Complex Numbers

The standard form of a complex number is typically written as a + bi, where 'a' and 'b' are real numbers. When performing operations with complex numbers, such as addition or subtraction, it is important to combine like terms (real with real and imaginary with imaginary) to express the result in this standard form. This ensures clarity and consistency in mathematical communication.

Video consigliato:

05:02

Multiplying Complex Numbers

Pratica correlata

Domanda del libro di testo

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. 3/(2x - 2) + 1/2 = 2/(x - 1)

1074

views

Domanda del libro di testo

1168

views

Domanda del libro di testo

Solve each equation in Exercises 47–64 by completing the square. $x^{2} - 5 x + 6 = 0$

801

views

Domanda del libro di testo

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)² - 4(x - 5) - 21 = 0

639