Skip to main content
Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 41
Capitolo 2, Problema 41

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 2 + √-4)2

Guida verificata passo dopo passo
1
Step 1: Recognize that the expression involves a square of a binomial, (-2 + √-4)^2. To simplify, use the formula for the square of a binomial: (a + b)^2 = a^2 + 2ab + b^2.
Step 2: Identify the terms in the binomial. Here, a = -2 and b = √-4. Note that √-4 involves the imaginary unit i, since the square root of a negative number is not defined in the real numbers. Rewrite √-4 as 2i, where i = √-1.
Step 3: Substitute the values of a and b into the formula. The expression becomes (-2)^2 + 2(-2)(2i) + (2i)^2.
Step 4: Simplify each term. (-2)^2 = 4, 2(-2)(2i) = -8i, and (2i)^2 = 4i^2. Recall that i^2 = -1, so 4i^2 = 4(-1) = -4.
Step 5: Combine the simplified terms. Add the real parts (4 and -4) and the imaginary part (-8i) to write the result in standard form, which is a + bi, where a is the real part and b is the coefficient of the imaginary part.

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:
3m

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 seen in this problem.
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 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 applications in various fields, including engineering and physics.
Video consigliato:
05:02
Multiplying Complex Numbers

Exponentiation of Complex Numbers

Exponentiation of complex numbers involves raising a complex number to a power, which can be done using the distributive property and the properties of exponents. In this case, squaring the complex number requires applying the formula (a + bi)² = a² + 2abi + (bi)², where (bi)² equals -b². This process is crucial for simplifying the expression and obtaining the result in standard form.
Video consigliato:
04:22
Dividing Complex Numbers
Pratica correlata
Domanda del libro di testo

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

778
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. x2−7xx^2 - 7x

977
views
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. 4/x = 5/2x + 3

972
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. x2 + 3x

1236
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 - 3/2 ≤ x/2 + 1

822
views
Domanda del libro di testo

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? E = mc2 for m

688
views