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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![### Complex Numbers: Transformation and Plotting
#### Write the standard form of the complex number.
Given the complex number:
\[ 5 (\cos(135^\circ) + i \sin(135^\circ)) \]
Please enter the complex number in its standard form:
\[ \boxed{} \]
#### Plot the complex number.
Select the correct graph from the options below that represents the given complex number:.
1. **First Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the second quadrant around approximate coordinates (-3.54, 3.54).
2. **Second Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the fourth quadrant around approximate coordinates (3.54, -3.54).
3. **Third Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the second quadrant around approximate coordinates (-3.54, -3.54).
4. **Fourth Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the third quadrant around approximate coordinates (-3.54, -3.54).
Choose the correct option that accurately represents the given complex number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e326e69-8929-40ad-94ce-3b7766681b63%2Faad6fe2d-caa3-49ac-a432-4d7b5eca2a09%2Fcxjm6j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Complex Numbers: Transformation and Plotting
#### Write the standard form of the complex number.
Given the complex number:
\[ 5 (\cos(135^\circ) + i \sin(135^\circ)) \]
Please enter the complex number in its standard form:
\[ \boxed{} \]
#### Plot the complex number.
Select the correct graph from the options below that represents the given complex number:.
1. **First Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the second quadrant around approximate coordinates (-3.54, 3.54).
2. **Second Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the fourth quadrant around approximate coordinates (3.54, -3.54).
3. **Third Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the second quadrant around approximate coordinates (-3.54, -3.54).
4. **Fourth Graph:**
- **Axes:**
- Vertical axis labeled "Imaginary axis".
- Horizontal axis labeled "Real axis".
- Both axes range from -5 to 5.
- **Plot:**
- Point plotted in the third quadrant around approximate coordinates (-3.54, -3.54).
Choose the correct option that accurately represents the given complex number.
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