/*! 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 49 Explain how to divide complex nu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 49

Explain how to divide complex numbers. Provide an example with your explanation.

Short Answer

Expert verified
To divide complex numbers, write them in standard form, multiply top and bottom by the conjugate of the denominator and then simplify. For example, to divide (2 + 3i) by (1 - 2i), the answer is \( 4/3 - 7/3 * i \).

Step by step solution

01

Complex number definition

Identify the real (a and c) and the imaginary parts (b and d) of both complex numbers. For instance, let's say we want to divide (2 + 3i) by (1 - 2i).
02

Find the Conjugate of the Denominator

In this case, the conjugate of the denominator (1 - 2i) is (1 + 2i) since we change the sign in the middle.
03

Multiply Numerator and Denominator by the Conjugate

Carry out the multiplication, treating 'i' as a variable and remembering that \(i^2 = -1\). This should give you: \((2+3i)\times(1+2i)\) and \((1-2i)\times(1+2i)\) which translates to \((2+4i+3i+6i^2) \over (1+2i-2i-4i^2)\) after multiplication.
04

Simplify the Equation

In the numerator, combine like terms and convert \(i^2\) to \(-1\) and do the same for the denominator. This simplifies to \( 2 + 7i - 6 \over 1 - 4 \), which simplifies further to \(-4 + 7i \over -3\).
05

Final Answer

The final step is to divide every term by -3 (the real number in the denominator), the answer will be \( 4/3 - 7/3 * i \).

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!

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

In Exercises \(69-72,\) use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$ \frac{1}{(x-2)^{2}}>0 $$

In Exercises \(1-8,\) add or subtract as indicated and write the result in standard form. $$(7+2 i)+(1-4 i)$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{3 x+5}{6-2 x} \geq 0 $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(7-5 i)(-2-3 i)$$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(5-2 i)^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.