Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7
900
views
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 73
Evaluate (x2 + 19)/(2 - x) for x = 3i.
Guida verificata passo dopo passo1
Substitute x = 3i into the given expression (x^2 + 19)/(2 - x). This means replacing every occurrence of x with 3i.
Simplify the numerator x^2 + 19. First, calculate (3i)^2, which involves squaring the imaginary number 3i. Recall that i^2 = -1, so (3i)^2 = 9i^2 = 9(-1) = -9. Add this result to 19 to simplify the numerator.
Simplify the denominator 2 - x. Replace x with 3i, so the denominator becomes 2 - 3i.
Combine the simplified numerator and denominator into the fraction. The expression now takes the form of a complex fraction with a real part and an imaginary part.
If necessary, rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator (2 + 3i). This step eliminates the imaginary part in the denominator, leaving a simplified complex number.
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:
5mConcetti 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. In this question, '3i' is a purely imaginary number, which means its real part is zero.
Video consigliato:
04:22
Dividing Complex Numbers
Polynomial Evaluation
Polynomial evaluation involves substituting a specific value into a polynomial expression to compute its value. In this case, the expression (x^2 + 19) is a polynomial, and we need to evaluate it by substituting x with 3i, which requires calculating (3i)^2 and then adding 19.
Video consigliato:
05:13Introduction to Polynomials
Rational Functions
A rational function is a function that can be expressed as the ratio of two polynomials. In this question, the expression (x^2 + 19)/(2 - x) is a rational function, and evaluating it at x = 3i involves calculating both the numerator and the denominator separately before performing the division.
Video consigliato:
6:04Intro to Rational Functions
Pratica correlata
Domanda del libro di testo
Solve each equation in Exercises 65–74 using the quadratic formula. x2 - 6x + 10 = 0
1032
views
Domanda del libro di testo
In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3
899
views
Domanda del libro di testo
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x
938
views
Domanda del libro di testo
Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)
908
views
Domanda del libro di testo
Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8
907
views