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Plot the complex number and its complex conjugate. 9 - 6i Imaginary axis 10- 8

Plot the complex number and its complex conjugate. 9 - 6i Imaginary axis 10- 8

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Plotting Complex Numbers and Their Conjugates** ### Example: Plotting the Complex Number \( 9 - 6i \) **Task:** Plot the complex number and its complex conjugate on the complex plane. **Given Complex Number:** \[ 9 - 6i \] **Steps to Plot:** 1. **Identify the Components:** - Real part (x-coordinate): \(9\) - Imaginary part (y-coordinate): \( -6 \) 2. **Plotting the Complex Number:** - On the complex plane, find the point (9, -6). - This point corresponds to moving \(9\) units to the right on the Real (horizontal) axis and \(6\) units down on the Imaginary (vertical) axis. 3. **Complex Conjugate:** - The complex conjugate of \(9 - 6i\) is \(9 + 6i\). - This switches the sign of the imaginary part. 4. **Plotting the Complex Conjugate:** - On the complex plane, find the point (9, 6). - This point corresponds to moving \(9\) units to the right on the Real (horizontal) axis and \(6\) units up on the Imaginary (vertical) axis. **Diagram Description:** The image shows a section of the complex plane with the following features: - The vertical axis is labeled "Imaginary axis" with increments of 2, starting from 8 and going up to 10. - The horizontal axis (Real axis) is not visible in the provided image segment. - The cursor points towards the plot area. By following these steps and using the diagram above as a guide, you can effectively plot both the complex number \(9 - 6i\) and its complex conjugate \(9 + 6i\) on the complex plane.
Transcribed Image Text:**Plotting Complex Numbers and Their Conjugates** ### Example: Plotting the Complex Number \( 9 - 6i \) **Task:** Plot the complex number and its complex conjugate on the complex plane. **Given Complex Number:** \[ 9 - 6i \] **Steps to Plot:** 1. **Identify the Components:** - Real part (x-coordinate): \(9\) - Imaginary part (y-coordinate): \( -6 \) 2. **Plotting the Complex Number:** - On the complex plane, find the point (9, -6). - This point corresponds to moving \(9\) units to the right on the Real (horizontal) axis and \(6\) units down on the Imaginary (vertical) axis. 3. **Complex Conjugate:** - The complex conjugate of \(9 - 6i\) is \(9 + 6i\). - This switches the sign of the imaginary part. 4. **Plotting the Complex Conjugate:** - On the complex plane, find the point (9, 6). - This point corresponds to moving \(9\) units to the right on the Real (horizontal) axis and \(6\) units up on the Imaginary (vertical) axis. **Diagram Description:** The image shows a section of the complex plane with the following features: - The vertical axis is labeled "Imaginary axis" with increments of 2, starting from 8 and going up to 10. - The horizontal axis (Real axis) is not visible in the provided image segment. - The cursor points towards the plot area. By following these steps and using the diagram above as a guide, you can effectively plot both the complex number \(9 - 6i\) and its complex conjugate \(9 + 6i\) on the complex plane.
### Writing the Conjugate of a Complex Number **Instruction:** Write the conjugate as a complex number. --- #### Explanation: In this task, you are asked to determine the conjugate of a given complex number and write it accordingly in the provided space. **What is a Complex Number?** A complex number is expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit with the property that \( i^2 = -1 \). **What is the Conjugate of a Complex Number?** The conjugate of a complex number \( a + bi \) is \( a - bi \). This essentially means you change the sign of the imaginary part. For example: - If the complex number is \( 3 + 4i \), its conjugate is \( 3 - 4i \). - If the complex number is \( -2 + 5i \), its conjugate is \( -2 - 5i \). Use the input box provided to write down the conjugate of the given complex number. --- In the image, a short instruction "Write the conjugate as a complex number." is displayed with an empty box below it. This is where the user is supposed to input the conjugate of a given complex number.
Transcribed Image Text:### Writing the Conjugate of a Complex Number **Instruction:** Write the conjugate as a complex number. --- #### Explanation: In this task, you are asked to determine the conjugate of a given complex number and write it accordingly in the provided space. **What is a Complex Number?** A complex number is expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit with the property that \( i^2 = -1 \). **What is the Conjugate of a Complex Number?** The conjugate of a complex number \( a + bi \) is \( a - bi \). This essentially means you change the sign of the imaginary part. For example: - If the complex number is \( 3 + 4i \), its conjugate is \( 3 - 4i \). - If the complex number is \( -2 + 5i \), its conjugate is \( -2 - 5i \). Use the input box provided to write down the conjugate of the given complex number. --- In the image, a short instruction "Write the conjugate as a complex number." is displayed with an empty box below it. This is where the user is supposed to input the conjugate of a given complex number.
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