**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.

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Answered: Plot the complex number and its complex…

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

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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Question

**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.

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