/*! 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 28 Divide and express the result in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 28

Divide and express the result in standard form. $$ \frac{3-4 i}{4+3 i} $$

Short Answer

Expert verified
The result in standard form of the division is \(\frac{24}{25} - \frac{21i}{25}\).

Step by step solution

01

Identifying the Conjugate

The conjugate of the denominator \(4+3i\) is \(4-3i\). In the conjugate, the sign of the imaginary part is reversed.
02

Multiply with the Conjugate

Next, multiply both the numerator and the denominator by the conjugate, \(4-3i\). This gives the expression \(\frac{(3-4i)(4-3i)}{(4+3i)(4-3i)}\).
03

Calculating the Numerator and Denominator

By multiplying, the numerator becomes \(3*4 + 3*-3i -4*3i +( -4i)*(-3i)\) and the denominator becomes \(4*4 + 4*-3i +3i*4 +(3i)*(-3i)\).
04

Simplifying the Numerator and Denominator

Simplify both the numerator and the denominator to get \(12-9i-12i+12\) and \(16-12i+12i+9\). To note here, \(i^2\)= -1 . So, simplifying it further gives \(24-21i\) and \(25\).
05

Express the Result in Standard Form

Lastly, divide the numerator by 25 to express the result in the standard form. It gives \(\frac{24}{25} - \frac{21i}{25}\). This is the standard form of the result.

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

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88 . There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90 . a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.

Solve absolute value inequality. \(1<|2-3 x|\)

A basic cellphone plan costs \(\$ 20\) per month for 60 calling minutes. Additional time costs \(\$ 0.40\) per minute. The formula $$C-20+0.40(x-60)$$ gives the monthly cost for this plan, \(C\), for \(x\) calling minutes, where \(x>60 .\) How many calling minutes are possible for a monthly cost of at least \(\$ 28\) and at most \(\$ 40 ?\)

Solve absolute value inequality. \(4<|2-x|\)

Solve absolute value inequality. \(|x|>3\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

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.