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Given the fact that i, the imaginary unit, is -1, what will be the value of 4i462 O 4 Q4 Simplify 4i -4i -1/24;- (5/4)i O -1/24; + (5/4)i O 1/22; - 1/22; i 1/22; + 1/22; i of 5 iWhat is the product of: (3 - 4) and (-21 - 61) ? -84 + 24i -84 - 24i 87 + 66i -87 + 661 F10

Given the fact that i, the imaginary unit, is -1, what will be the value of 4i462 O 4 Q4 Simplify 4i -4i -1/24;- (5/4)i O -1/24; + (5/4)i O 1/22; - 1/22; i 1/22; + 1/22; i of 5 iWhat is the product of: (3 - 4) and (-21 - 61) ? -84 + 24i -84 - 24i 87 + 66i -87 + 661 F10

Calculus: Early Transcendentals
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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## Understanding the Complex Plane ### Problem Statement: In the complex plane, what is the value of the following point \( z? \) ### Explanation: The given image contains a graph representing the complex plane with a point plotted on it. The complex plane has a horizontal axis labeled with real numbers and a vertical axis labeled with imaginary numbers. The point \( z \) is marked, and there are answer choices provided. #### Steps to Solve: 1. **Identify the Coordinates:** - Locate the plotted point on the complex plane to determine its coordinates. - The x-axis represents the real part of the complex number. - The y-axis represents the imaginary part of the complex number (usually denoted with an \(i\)). 2. **Determine the Value of \( z \):** - The coordinates provide the real and imaginary parts which can be expressed in the form \( a + bi \). #### Given Answer Choices: 1. \( -2 - 45i \) 2. \( 3 - 45i \) 3. \( -2 + 3i \) 4. \( 3 - 21i \) Using the graph, let’s identify the position of the point \( z \). ### Graph Analysis: The complex point appears to be located at the coordinates: - Real part: -2 - Imaginary part: -45 (i.e., 45 units down the vertical axis) Thus, the correct value of \( z \) in the complex plane would be \( -2 - 45i \). ### Conclusion: The correct answer is: \[ \boxed{-2 - 45i} \] ### Additional Note: Understanding how to read and interpret points on the complex plane is essential for solving problems involving complex numbers. The complex plane allows for a visual representation of complex numbers, making it easier to grasp their properties and interactions.
Transcribed Image Text:## Understanding the Complex Plane ### Problem Statement: In the complex plane, what is the value of the following point \( z? \) ### Explanation: The given image contains a graph representing the complex plane with a point plotted on it. The complex plane has a horizontal axis labeled with real numbers and a vertical axis labeled with imaginary numbers. The point \( z \) is marked, and there are answer choices provided. #### Steps to Solve: 1. **Identify the Coordinates:** - Locate the plotted point on the complex plane to determine its coordinates. - The x-axis represents the real part of the complex number. - The y-axis represents the imaginary part of the complex number (usually denoted with an \(i\)). 2. **Determine the Value of \( z \):** - The coordinates provide the real and imaginary parts which can be expressed in the form \( a + bi \). #### Given Answer Choices: 1. \( -2 - 45i \) 2. \( 3 - 45i \) 3. \( -2 + 3i \) 4. \( 3 - 21i \) Using the graph, let’s identify the position of the point \( z \). ### Graph Analysis: The complex point appears to be located at the coordinates: - Real part: -2 - Imaginary part: -45 (i.e., 45 units down the vertical axis) Thus, the correct value of \( z \) in the complex plane would be \( -2 - 45i \). ### Conclusion: The correct answer is: \[ \boxed{-2 - 45i} \] ### Additional Note: Understanding how to read and interpret points on the complex plane is essential for solving problems involving complex numbers. The complex plane allows for a visual representation of complex numbers, making it easier to grasp their properties and interactions.
**Unit 2 Lesson on Complex Numbers** **Assessment Questions and Solutions** 1. **What is the product of: (3 - 4i) and (-21 - 6i)?** - ☐ -84 + 24i - ☐ -84 - 24i - ☐ 87 + 66i - ☐ -87 + 66i 2. **Given the fact that i, the imaginary unit, is \(\sqrt{-1}\), what will be the value of \(4i^{46}\)?** - ☐ 4 - ☐ -4 - ☐ 4i - ☐ -4i 3. **Simplify \(\frac{\frac{7}{2} - \frac{3i}{2}}{2 + 2i}\):** - ☐ \(\frac{-1}{24}; \frac{-(5/4)}{i}\) - ☐ \(\frac{-1}{24}; \frac{(5/4)}{i}\) - ☐ \(\frac{1}{22}; \frac{1}{22i}\) - ☐ \(\frac{1}{22}; \frac{1}{22}; i\) - ☐ \(\frac{1}{22}; \frac{1}{22}; + 1/22i\) 4. **What is the sum of: (3 - 4i) and (-21 - 6i)?** - ☐ -24 - 10i - ☐ 18 - 2i - ☐ -18 - 10i - ☐ 24 + 2i This lesson covers the fundamental operations on complex numbers, including their addition, multiplication, and the simplification of expressions involving imaginary numbers. For answers and detailed solutions, refer to the unit's tutorial videos and notes. Always ensure you understand each step when working with complex numbers to build a strong mathematical foundation in this topic.
Transcribed Image Text:**Unit 2 Lesson on Complex Numbers** **Assessment Questions and Solutions** 1. **What is the product of: (3 - 4i) and (-21 - 6i)?** - ☐ -84 + 24i - ☐ -84 - 24i - ☐ 87 + 66i - ☐ -87 + 66i 2. **Given the fact that i, the imaginary unit, is \(\sqrt{-1}\), what will be the value of \(4i^{46}\)?** - ☐ 4 - ☐ -4 - ☐ 4i - ☐ -4i 3. **Simplify \(\frac{\frac{7}{2} - \frac{3i}{2}}{2 + 2i}\):** - ☐ \(\frac{-1}{24}; \frac{-(5/4)}{i}\) - ☐ \(\frac{-1}{24}; \frac{(5/4)}{i}\) - ☐ \(\frac{1}{22}; \frac{1}{22i}\) - ☐ \(\frac{1}{22}; \frac{1}{22}; i\) - ☐ \(\frac{1}{22}; \frac{1}{22}; + 1/22i\) 4. **What is the sum of: (3 - 4i) and (-21 - 6i)?** - ☐ -24 - 10i - ☐ 18 - 2i - ☐ -18 - 10i - ☐ 24 + 2i This lesson covers the fundamental operations on complex numbers, including their addition, multiplication, and the simplification of expressions involving imaginary numbers. For answers and detailed solutions, refer to the unit's tutorial videos and notes. Always ensure you understand each step when working with complex numbers to build a strong mathematical foundation in this topic.
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