/*! 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 \(2-3i\) and when they are multiplied, the result is 13.

Step by step solution

01

Find the Complex Conjugate

The complex conjugate of a complex number has the same real part and the imaginary part with the opposite sign. So, the complex conjugate of \(2+3i\) is \(2-3i\)
02

Multiply the Complex Number by its Conjugate

To multiply the original number with its conjugate, we use the algebraic rule \((a+b) * (a-b) = a^2 - b^2\) resulting in \( (2+3i) * (2-3i) = 2^2 - (3i)^2 = 4 - (-9) = 4 + 9 = 13 \)
03

Answer

Therefore, when \(2+3i\) is multiplied by its complex conjugate \(2-3i\), we get 13

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

List all numbers that must be excluded from the domain of each rational expression. $$ \frac{3}{2 x^{2}+4 x-9} $$

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.

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ (-\infty, 3) \cup(-\infty,-2)=(-\infty,-2) $$

In Exercises 142鈥�143, solve each inequality using a graphing utility. Graph each side separately. Then determine the values of x for which the graph for the left side lies above the graph for the right side. $$ -3(x-6)>2 x-2 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.