/*! 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 61 What is the complex conjugate of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 61

What is the complex conjugate of \(2+3 i ?\) What happens when you multiply this complex number by its complex conjugate?

Short Answer

Expert verified
The complex conjugate of \(2+3i\) is \(2-3i\). When you multiply this complex number by its complex conjugate, the result is \(-5\).

Step by step solution

01

Find the Complex Conjugate

The complex conjugate of a complex number is obtained by flipping the sign of its imaginary part. The given complex number is \(2+3 i\), so the complex conjugate will be \(2-3 i\).
02

Multiply the Complex Number by its Conjugate

To multiply two complex numbers, distribute the product across each term following the rule \(i^2=-1\). Therefore, \((2 + 3i) * (2 - 3i) = 2*2 + 2*-3i + 3i*2 -3i*-3i = 4 - 6i + 6i -9 = 4 - 9 = -5\).
03

Final Answer

The complex number \(2 + 3i\) multiplied by its complex conjugate \(2 - 3i\) equals to \(-5\). The result isn't a complex number because the imaginary parts cancelled out. This is a property of a complex number multiplied by its conjugate: it always results a real number.

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. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

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

Describe the solution set of \(|x|>-4\).

Solve absolute value inequality. \(\left|3-\frac{3}{4} x\right|>9\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(1-\frac{x}{2}>4\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.