cis
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
How do I multiply this and leave it in trigonometric form? (Do not use cis form)
![The image contains the mathematical expression:
\[ 5 \cdot \text{cis} \left( \frac{\pi}{7} \right) \cdot 7 \cdot \text{cis} \left( \frac{\pi}{7} \right) \]
**Explanation for an Educational Website:**
The expression involves multiplying complex numbers in polar form. In polar form, a complex number can be represented as \( r \cdot \text{cis}(\theta) \), where \( r \) is the magnitude (or modulus) and \( \theta \) is the angle (or argument).
In this specific case:
- We have two complex numbers: \( 5 \cdot \text{cis} \left( \frac{\pi}{7} \right) \) and \( 7 \cdot \text{cis} \left( \frac{\pi}{7} \right) \).
- The magnitude of the first number is 5, and the second number is 7.
- Both have the same angle \( \frac{\pi}{7} \).
When multiplying two complex numbers in polar form, you multiply their magnitudes and add their angles. So:
1. Multiply the magnitudes: \( 5 \times 7 = 35 \).
2. Add the angles: \( \frac{\pi}{7} + \frac{\pi}{7} = \frac{2\pi}{7} \).
Thus, the product is:
\[ 35 \cdot \text{cis} \left( \frac{2\pi}{7} \right) \]
This result represents the new complex number in polar form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffcaf5a2f-30f3-43ad-aa15-f0ef70a8b313%2F8680867c-9002-444b-a7fb-b449b949094d%2Fpznq34c.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains the mathematical expression:
\[ 5 \cdot \text{cis} \left( \frac{\pi}{7} \right) \cdot 7 \cdot \text{cis} \left( \frac{\pi}{7} \right) \]
**Explanation for an Educational Website:**
The expression involves multiplying complex numbers in polar form. In polar form, a complex number can be represented as \( r \cdot \text{cis}(\theta) \), where \( r \) is the magnitude (or modulus) and \( \theta \) is the angle (or argument).
In this specific case:
- We have two complex numbers: \( 5 \cdot \text{cis} \left( \frac{\pi}{7} \right) \) and \( 7 \cdot \text{cis} \left( \frac{\pi}{7} \right) \).
- The magnitude of the first number is 5, and the second number is 7.
- Both have the same angle \( \frac{\pi}{7} \).
When multiplying two complex numbers in polar form, you multiply their magnitudes and add their angles. So:
1. Multiply the magnitudes: \( 5 \times 7 = 35 \).
2. Add the angles: \( \frac{\pi}{7} + \frac{\pi}{7} = \frac{2\pi}{7} \).
Thus, the product is:
\[ 35 \cdot \text{cis} \left( \frac{2\pi}{7} \right) \]
This result represents the new complex number in polar form.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning