/*! 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 21 Divide and express the result in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 21

Divide and express the result in standard form. $$\frac{2}{3-i}$$

Short Answer

Expert verified
The answer is \(0.6 + 0.2i\)

Step by step solution

01

Identify the conjugate

The conjugate of a complex number \(a + bi\) is \(a - bi\). So, in this case, the conjugate of \(3 - i\) is \(3 + i\)
02

Multiply the numerator and denominator by the conjugate

Multiply both the numerator and denominator by \(3 + i\). This gives \[\frac{2*(3 + i)}{(3 - i)*(3 + i)}\]
03

Distribute in the numerator

Distribute the 2 in the numerator. This gives the expression \[\frac{6 + 2i}{(3 - i)*(3 + i)}\]
04

Multiply out the denominator

Now multiply out the denominator. When you multiply out conjugates, the result is \[a^2 + b^2\]. So, the expression becomes: \[\frac{6 + 2i}{9 + 1}\]
05

Simplify

Simplify to reach the result \[\frac{6+2i}{10}\]. Simplify further to get in standard form \(a + bi\) as \(0.6 + 0.2i\)

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

Begin by deciding on a product that interests the group because you are now in charge of advertising this product. Members were told that the demand for the product varies directly as the amount spent on advertising and inversely as the price of the product. However, as more money is spent on advertising, the price of your product rises. Under what conditions would members recommend an increased expense in advertising? Once you've determined what your product is, write formulas for the given conditions and experiment with hypothetical numbers. What other factors might you take into consideration in terms of your recommendation? How do these factors affect the demand for your product?

Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has a vertical asymptote given by \(x=1,\) a slant asymptote whose equation is \(y=x, y\) -intercept at \(2,\) and \(x\)-intercepts at -1 and 2.

Find the domain of \(h(x)=\sqrt{36-2 x}\).

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$(x)=\frac{1}{(x+2)^{2}}$$

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{3 x+7}{x+2}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.