/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 54 Evaluate \(\frac{x^{2}+11}{3-x}\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 54

Evaluate \(\frac{x^{2}+11}{3-x}\) for \(x=4 i\)

Short Answer

Expert verified
Thus, \(\frac{x^{2}+11}{3-x}\) evaluates to \(-\frac{3}{5} - \frac{4}{5}i\) for \(x=4 i\).

Step by step solution

01

Substitute the value of x

Start by substituting \(x = 4i\) into the function \(\frac{x^{2}+11}{3-x}\), this gives \(\frac{(4i)^{2}+11}{3-(4i)} = \frac{-16+11}{3-4i}\), since \(i^{2} = -1\).
02

Simplify the numerator

Simplify the numerator to get \(-5\) resulting to \(\frac{-5}{3-4i}\).
03

Rationalize the denominator

Multiply both numerator and denominator by the conjugate of \(3-4i\), which is \(3+4i\). Now you have \(\frac{-5(3 + 4i)}{(3-4i)(3+4i)}\).
04

Apply foil method to the denominator

Expand the denominator using FOIL: \(3*3 -3*4i +3*4i -(4i)^2\). This simplifies to \(9+16 = 25\), resulting in \(\frac{-5(3 + 4i)}{25}\).
05

Simplify the expression

Finally, simplify the expression by distributing the -5 to both terms in the numerator and dividing by 25: \(\frac{-15 - 20i}{25} = -\frac{3}{5} - \frac{4}{5}i\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is a quadratic equation?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set, I should obtain a true statement, and when 0 does not belong to the solution set, I should obtain a false statement.

The formula for converting Fahrenheit temperature, \(F,\) to Celsius temperature, \(C,\) is $$ C=\frac{5}{9}(F-32) $$ If Celsius temperature ranges from \(15^{\circ}\) to \(35^{\circ},\) inclusive, what is the range for the Fahrenheit temperature? Use interval notation to express this range.

When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. Use interval notation to express the set of all numbers that satisfy this condition.

Describe the relationship between the real solutions of \(a x^{2}+b x+c=0\) and the graph of \(y=a x^{2}+b x+c\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.