/*! 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 39 Add or subtract as indicated. Gi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 39

Add or subtract as indicated. Give answers in standard form. $$(3+2 i)+(-4+5 i)$$

Short Answer

Expert verified
-1 + 7i

Step by step solution

01

- Identify real and imaginary parts

Identify the real and imaginary parts of each complex number. For (3 + 2i), the real part is 3 and the imaginary part is 2i. For (-4 + 5i), the real part is -4 and the imaginary part is 5i.
02

- Add the real parts

Add the real parts of the complex numbers: 3 + (-4) = -1.
03

- Add the imaginary parts

Add the imaginary parts of the complex numbers: 2i + 5i = 7i.
04

- Combine the results

Combine the results from Steps 2 and 3 to form the final complex number: -1 + 7i.

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.

real part
The real part of a complex number is the non-imaginary component. Complex numbers are typically written in the form \(a + bi\), where \(a\) is the real part and \(bi\) is the imaginary part. For example, in the complex number \(3 + 2i\), the real part is \(3\). Similarly, in \(-4 + 5i\), the real part is \(-4\).Understanding the real part is crucial for performing operations like addition and subtraction of complex numbers. In our exercise, we first identified the real parts of the numbers \(3 + 2i\) and \(-4 + 5i\). We found that they are \(3\) and \(-4\) respectively. We then added these real parts: \(3 + (-4) = -1\).
imaginary part
The imaginary part of a complex number is the component that includes the imaginary unit \(i\), where \(i\) is defined as \(\sqrt{-1}\). A complex number is written as \(a + bi\). In this expression, \(bi\) is the imaginary part. For example, in \(3 + 2i\), the imaginary part is \2i\. In \(-4 + 5i\), the imaginary part is \5i\.Imaginary parts are essential for operations on complex numbers. In the exercise, we identified the imaginary parts \2i\ and \5i\. We then added these imaginary components: \2i + 5i = 7i\. This shows how imaginary parts are handled similarly to real parts in addition.
addition of complex numbers
Adding complex numbers involves separately adding their real parts and their imaginary parts. Given two complex numbers \(a + bi\) and \(c + di\), their sum is \((a + c) + (b + d)i\).Following this method in the exercise, we first added the real parts: \3 + (-4) = -1\. Next, we added the imaginary parts: \2i + 5i = 7i\.Finally, we combined these results to get the sum: \-1 + 7i\. This result is the standard form of a complex number after addition. It's vital to treat real and imaginary parts separately to simplify and correctly carry out the operations.

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

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}} $$

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \frac{\sqrt[4]{w^{3}}}{\sqrt[6]{w}} $$

Write each quotient in lowest terms. Assume that all variables represent positive real numbers. $$ \frac{16-4 \sqrt{8}}{12} $$

Rationalize each denominator. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{242 t^{9}}{u^{11}}} $$

Write each quotient in lowest terms. Assume that all variables represent positive real numbers. $$ \frac{11 y-\sqrt{242 y^{5}}}{22 y} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

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.