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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Question
![**Transcription and Explanation:**
**Problem Statement:**
Find the distance \( d \) (in the complex plane) between \( z = 2 + 7i \) and \( w = 11 - 10i \).
**Calculation Attempt:**
The distance \( d \) is calculated as:
\[ d = \sqrt{(1)^2 + (9)^2} \]
However, a red "X" indicates that this calculation is incorrect.
**Explanation:**
To find the distance between two complex numbers \( z = a + bi \) and \( w = c + di \), use the distance formula for the complex plane:
\[ d = \sqrt{(c - a)^2 + (d - b)^2} \]
In this problem, correct \( a = 2 \), \( b = 7 \), \( c = 11 \), and \( d = -10 \). The components should be:
\[ c - a = 11 - 2 = 9 \]
\[ d - b = -10 - 7 = -17 \]
The correct calculation should be:
\[ d = \sqrt{(9)^2 + (-17)^2} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0cfd4d2-3b60-4b70-8ad1-e02fd206eb06%2Fa47d7402-fdc5-4e09-a970-ab63e6de044a%2Fkn6dhj9_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation:**
**Problem Statement:**
Find the distance \( d \) (in the complex plane) between \( z = 2 + 7i \) and \( w = 11 - 10i \).
**Calculation Attempt:**
The distance \( d \) is calculated as:
\[ d = \sqrt{(1)^2 + (9)^2} \]
However, a red "X" indicates that this calculation is incorrect.
**Explanation:**
To find the distance between two complex numbers \( z = a + bi \) and \( w = c + di \), use the distance formula for the complex plane:
\[ d = \sqrt{(c - a)^2 + (d - b)^2} \]
In this problem, correct \( a = 2 \), \( b = 7 \), \( c = 11 \), and \( d = -10 \). The components should be:
\[ c - a = 11 - 2 = 9 \]
\[ d - b = -10 - 7 = -17 \]
The correct calculation should be:
\[ d = \sqrt{(9)^2 + (-17)^2} \]
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