Homework Help is Here – Start Your Trial Now!
Math
Algebra
practice 4+3₁ 2-Si

practice 4+3₁ 2-Si

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
### Understanding Complex Conjugates In mathematics, particularly in the field of complex numbers, the **complex conjugate** of a complex number is important for simplifying expressions and solving equations. The complex conjugate of a number in the form \(a + bi\) is written as \(a - bi\). #### Practice Problem Consider the following expression which involves complex numbers: \[ \frac{4 + 3i}{2 - 5i} \] To simplify this expression, the technique involves multiplying the numerator and the denominator by the conjugate of the denominator. This process is necessary to eliminate the imaginary component from the denominator. Here’s a step-by-step approach: 1. **Identify the conjugate of the denominator:** The complex conjugate of \(2 - 5i\) is \(2 + 5i\). 2. **Multiply both the numerator and the denominator by this conjugate:** \[ \frac{(4 + 3i)(2 + 5i)}{(2 - 5i)(2 + 5i)} \] 3. **Simplify your result using the identity \((a + bi)(a - bi) = a^2 + b^2\) for the denominator:** The use of the complex conjugate eliminates the imaginary part, simplifying calculations and leading to a rational result in the denominator. By practicing this problem, you will gain a firmer grasp on handling complex conjugates in mathematical operations.
Transcribed Image Text:### Understanding Complex Conjugates In mathematics, particularly in the field of complex numbers, the **complex conjugate** of a complex number is important for simplifying expressions and solving equations. The complex conjugate of a number in the form \(a + bi\) is written as \(a - bi\). #### Practice Problem Consider the following expression which involves complex numbers: \[ \frac{4 + 3i}{2 - 5i} \] To simplify this expression, the technique involves multiplying the numerator and the denominator by the conjugate of the denominator. This process is necessary to eliminate the imaginary component from the denominator. Here’s a step-by-step approach: 1. **Identify the conjugate of the denominator:** The complex conjugate of \(2 - 5i\) is \(2 + 5i\). 2. **Multiply both the numerator and the denominator by this conjugate:** \[ \frac{(4 + 3i)(2 + 5i)}{(2 - 5i)(2 + 5i)} \] 3. **Simplify your result using the identity \((a + bi)(a - bi) = a^2 + b^2\) for the denominator:** The use of the complex conjugate eliminates the imaginary part, simplifying calculations and leading to a rational result in the denominator. By practicing this problem, you will gain a firmer grasp on handling complex conjugates in mathematical operations.
Expert Solution
Step 1

NOTE: Refresh your page if you can't see any equations.

.

\frac{4+3i}{2-5i}

multiply and divide by (2+5i)

=\frac{4+3i}{2-5i}\cdot \frac{2+5i}{2+5i}

=\frac{\left(4+3i\right)\left(2+5i\right)}{\left(2-5i\right)\left(2+5i\right)}

steps

Step by step

Solved in 2 steps with 9 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS