Complete the following simplification. [3 (cos 315° + i sin 315°)] [2 (cos 45° + i sin 45°)] = (cos = + ... [3 (cos 315° + i sin 315°) ] [2 (cos 45° + i sin 45°)] = (cos + + i sin_____) + i sinº)
Complete the following simplification. [3 (cos 315° + i sin 315°)] [2 (cos 45° + i sin 45°)] = (cos = + ... [3 (cos 315° + i sin 315°) ] [2 (cos 45° + i sin 45°)] = (cos + + i sin_____) + i sinº)
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
![### Simplifying Complex Expressions in Polar Form
**Problem Statement:**
Complete the following simplification.
\[ \left[ 3 \left( \cos 315^\circ + i \sin 315^\circ \right) \right] \left[ 2 \left( \cos 45^\circ + i \sin 45^\circ \right) \right] = \underline{\hspace{1cm}} \left( \cos \underline{\hspace{1cm}} + i \sin \underline{\hspace{1cm}} \right) \]
\[ = \underline{\hspace{1cm}} + \underline{\hspace{1cm}} i \]
---
\[ \left[ 3 \left( \cos 315^\circ + i \sin 315^\circ \right) \right] \left[ 2 \left( \cos 45^\circ + i \sin 45^\circ \right) \right] = \left( \cos \underline{\hspace{1cm}}^\circ + i \sin \underline{\hspace{1cm}}^\circ \right) \]
\[ = \underline{\hspace{1cm}} + \underline{\hspace{1cm}} i \]
---
**Explanation of the Problem:**
We are given a problem where two complex numbers in polar form need to be multiplied. The expression is presented in the format:
\[
\left[ r_1 (\cos \theta_1 + i \sin \theta_1) \right] \left[ r_2 (\cos \theta_2 + i \sin \theta_2) \right]
\]
**Steps to Simplify:**
1. Identify the magnitudes \( r_1 \) and \( r_2 \):
- Here, \( r_1 = 3 \) and \( r_2 = 2 \).
2. Identify the angles \( \theta_1 \) and \( \theta_2 \):
- Here, \( \theta_1 = 315^\circ \) and \( \theta_2 = 45^\circ \).
3. Multiply the magnitudes:
\[
r = r_1 \times r_2 = 3 \times 2 = 6
\]
4. Add the angles:
\[
\theta = \theta_1 + \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3def50f-0bee-45b6-a067-ec9125eb6917%2F2b5975a6-9486-45dc-a406-7cbc37314889%2Fnz79sxd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Simplifying Complex Expressions in Polar Form
**Problem Statement:**
Complete the following simplification.
\[ \left[ 3 \left( \cos 315^\circ + i \sin 315^\circ \right) \right] \left[ 2 \left( \cos 45^\circ + i \sin 45^\circ \right) \right] = \underline{\hspace{1cm}} \left( \cos \underline{\hspace{1cm}} + i \sin \underline{\hspace{1cm}} \right) \]
\[ = \underline{\hspace{1cm}} + \underline{\hspace{1cm}} i \]
---
\[ \left[ 3 \left( \cos 315^\circ + i \sin 315^\circ \right) \right] \left[ 2 \left( \cos 45^\circ + i \sin 45^\circ \right) \right] = \left( \cos \underline{\hspace{1cm}}^\circ + i \sin \underline{\hspace{1cm}}^\circ \right) \]
\[ = \underline{\hspace{1cm}} + \underline{\hspace{1cm}} i \]
---
**Explanation of the Problem:**
We are given a problem where two complex numbers in polar form need to be multiplied. The expression is presented in the format:
\[
\left[ r_1 (\cos \theta_1 + i \sin \theta_1) \right] \left[ r_2 (\cos \theta_2 + i \sin \theta_2) \right]
\]
**Steps to Simplify:**
1. Identify the magnitudes \( r_1 \) and \( r_2 \):
- Here, \( r_1 = 3 \) and \( r_2 = 2 \).
2. Identify the angles \( \theta_1 \) and \( \theta_2 \):
- Here, \( \theta_1 = 315^\circ \) and \( \theta_2 = 45^\circ \).
3. Multiply the magnitudes:
\[
r = r_1 \times r_2 = 3 \times 2 = 6
\]
4. Add the angles:
\[
\theta = \theta_1 + \
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