/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 Find each sum or difference. Wri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 48

Find each sum or difference. Write the answer in standard form. $$(-4-i)-(2+3 i)+(-4+5 i)$$

Short Answer

Expert verified
-10 + i

Step by step solution

01

Identify the complex numbers

The given complex numbers are 1. -4-i 2. 2+3i 3. -4+5i
02

Distribute the subtraction

Apply the subtraction to the complex numbers: (-4-i)-(2+3i) + (-4+5i) = -4 - i -(2+3i) -4+5i .
03

Group real and imaginary parts

Group the real parts together and the imaginary parts together: (-4 - 2 - 4) + (-i - 3i + 5i) .
04

Simplify the real and imaginary parts

Simplify the real part: -4 - 2 - 4 = -10 . Simplify the imaginary part: -i - 3i + 5i = i .
05

Write the answer in standard form

Combine the simplified real and imaginary parts to get the final answer in standard form: -10 + i .

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Complex Number Addition
Adding complex numbers is just like adding two polynomial expressions. You add the real parts together and the imaginary parts together. For example, if you have two complex numbers: \(1 + 2i\) and \(3 + 4i\), you would first add the real parts (1 and 3) to get 4. Then, you add the imaginary parts (2i and 4i) to get 6i. So, the sum is \(4 + 6i\). When doing addition of complex numbers, always look to combine like terms. This makes simplifying much easier and ensures you get the correct result quickly.
Complex Number Subtraction
Subtracting complex numbers follows a similar pattern to addition, but you must remember that subtraction distributes across both the real and imaginary parts. Take the example: \((5 + 6i) - (3 + 2i)\). Start by subtracting the real parts: 5 minus 3 equals 2. Then, subtract the imaginary parts: 6i minus 2i equals 4i. Thus, \((5 + 6i) - (3 + 2i) = 2 + 4i\). Be cautious about the minus sign and ensure it applies to both parts of the complex number being subtracted.
Standard Form of Complex Numbers
Writing a complex number in its standard form means arranging it in the form \(a + bi\), where \(a\) is the real part and \(bi\) is the imaginary part. For instance, \(-1 + 2i\), where \(-1\) is the real part and \(2i\) is the imaginary part. This is helpful for clarity and ease of performing operations like addition and subtraction. When combining real and imaginary parts, always present your final answer in this form. For example, the result of the exercise, \(-10 + i\), is already in standard form, making it easy to understand and use for further calculations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each equation or inequality. $$|3 x+1|-1<2$$

Find each product. Write the answer in standard form. $$(3-i)(3+i)(2-6 i)$$

Solve each rational inequality. Write each solution set in interval notation.4 $$\frac{(5-3 x)^{2}}{(2 x-5)^{3}}>0$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{6+2 i}{1+2 i}$$

Find each product. Write the answer in standard form. $$(\sqrt{6}+i)(\sqrt{6}-i)$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.