Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Writing the Trigonometric Form of a Complex Number
In this section, learners will explore how to write a complex number in its trigonometric form. Ensure to round your angles to two decimal places as specified. Below are the instructions and an interactive component to practice this skill.
#### Instructions:
1. Convert the given complex number into its trigonometric form.
2. Round your angles to two decimal places.
3. Ensure that the angle \(\theta\) satisfies \(0 \leq \theta < 2\pi\).
The trigonometric form of a complex number \(z\) can be expressed as:
\[ z = r (\cos \theta + i \sin \theta) \]
Here, \(r\) is the magnitude of the complex number, and \(\theta\) is the argument (angle).
#### Interactive Practice:
**Write the trigonometric form of the complex number:**
\[ z = \_\_\_\_\_\_\_ \]
*Please input your answer in the box provided.*
---
**Explanation of Diagrams:**
The image includes three graphical symbols:
1. Two concentric circles at the top of the image, separated by some text or symbols.
2. Two additional circles, one with a checkmark, presumably indicating a multiple-choice or selection component.
The accompanying text reads:
"Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let \( 0 \leq \theta < 2\pi \))."
This interactive component is designed to help learners understand and apply the process of converting a complex number to its trigonometric form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fab864d-7419-4b8c-bc50-25971d273c3c%2F1f2bb9c4-ed82-41c9-9b31-9696bfcfaab6%2Fwmn068h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Writing the Trigonometric Form of a Complex Number
In this section, learners will explore how to write a complex number in its trigonometric form. Ensure to round your angles to two decimal places as specified. Below are the instructions and an interactive component to practice this skill.
#### Instructions:
1. Convert the given complex number into its trigonometric form.
2. Round your angles to two decimal places.
3. Ensure that the angle \(\theta\) satisfies \(0 \leq \theta < 2\pi\).
The trigonometric form of a complex number \(z\) can be expressed as:
\[ z = r (\cos \theta + i \sin \theta) \]
Here, \(r\) is the magnitude of the complex number, and \(\theta\) is the argument (angle).
#### Interactive Practice:
**Write the trigonometric form of the complex number:**
\[ z = \_\_\_\_\_\_\_ \]
*Please input your answer in the box provided.*
---
**Explanation of Diagrams:**
The image includes three graphical symbols:
1. Two concentric circles at the top of the image, separated by some text or symbols.
2. Two additional circles, one with a checkmark, presumably indicating a multiple-choice or selection component.
The accompanying text reads:
"Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let \( 0 \leq \theta < 2\pi \))."
This interactive component is designed to help learners understand and apply the process of converting a complex number to its trigonometric form.
![The image contains the mathematical expression:
\[ 7 \sqrt{7} - i \]
- **7** is a constant coefficient.
- **\(\sqrt{7}\)** represents the square root of 7.
- **-** is the subtraction operator.
- **\(i\)** denotes the imaginary unit, which is defined as \( \sqrt{-1} \).
This expression is part of complex numbers, where the real part is \( 7 \sqrt{7} \) and the imaginary part is \(-i\). Complex numbers are commonly used in advanced mathematics, engineering, and physics to solve equations that cannot be addressed by real numbers alone.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fab864d-7419-4b8c-bc50-25971d273c3c%2F1f2bb9c4-ed82-41c9-9b31-9696bfcfaab6%2Fle1tpx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains the mathematical expression:
\[ 7 \sqrt{7} - i \]
- **7** is a constant coefficient.
- **\(\sqrt{7}\)** represents the square root of 7.
- **-** is the subtraction operator.
- **\(i\)** denotes the imaginary unit, which is defined as \( \sqrt{-1} \).
This expression is part of complex numbers, where the real part is \( 7 \sqrt{7} \) and the imaginary part is \(-i\). Complex numbers are commonly used in advanced mathematics, engineering, and physics to solve equations that cannot be addressed by real numbers alone.
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