Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

In $46-60,$ write each quotient in $a+b i$ form.$$(2+4 i) \div(1-i)$$

$-1+3 i$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Missouri State University

Oregon State University

McMaster University

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

03:10

In $46-60,$ write each quo…

02:57

02:33

02:50

02:29

02:31

02:22

02:42

01:19

First of all, let's change this quotient into the following form two plus four I over one minus I and then to change it into standard form. What we can do is multiply the numerator and denominator by one plus I, which is the contra git of the denominator. This is going to help us to simplify the denominator. So we're going to multiply the enumerators by using the foil method. Multiply the first, the outsides, the insides and the last, and we get to plus two I plus four I plus four. I squared and then we multiply the denominators in the same way. But because they're congregates, the insides and outsides will cancel. So we'll end up with one minus. I squared. Now we want to do some simplifying. So in our numerator we can add the two y and the four I and that will give us six I and also remember that I squared is negative one. So we have four times negative. One on the bottom will also replace the I squared with negative one. So we one minus negative one. So we can simplify this because we have to plus four times negative one that's going to be to minus four. So that gives us negative two plus six. I over and the denominator will be, too. Now everything's divisible by two so we can change this to negative one plus three I

View More Answers From This Book

Find Another Textbook

In mathematics, the absolute value or modulus |x| of a real number x is its …

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{1+i}{\frac{1…

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{2+2 i}{4-2 i…

In $46-60,$ write each quotient in $a+b i$ form.$$(8+4 i) \div(1+i)<…

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{8+2 i}{1+3 i…

In $46-60,$ write each quotient in $a+b i$ form.$$(10+5 i) \div(1+2 …

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{8+6 i}{2 i}<…

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{10-5 i}{2+6 …

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{5-2 i}{5+2 i…

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{12+3 i}{3 i}…

In $46-60,$ write each quotient in $a+b i$ form.$$\frac{3+i}{3-i}

Ethan said that the square of any pure imaginary number is a negative real n…

01:45

Impedance is the resistance to the flow of current in an electric circuit me…

03:23

Ian often buys in large quantities. A few months ago he bought several cans …

00:23

In $3-18,$ write the first five terms of each sequence.$$a_{n}=3^{n}…

04:36

In $3-18,$ find all roots of each given function by factoring or by using th…

01:50

In $24-26,$ sketch the inverse of the given function.(SKETCH NOT COPY)

00:58

In $6-12,$ tell whether the variables vary directly, inversely, or neither.<…

00:46

Without solving each equation, find the sum and product of the roots.$x^…

00:42

In $3-5,$ each graph is a set of points whose $x$ -coordinates and $y$ -coor…

05:14

To solve the equation given in step 2 of Example 2 , Sarah multiplied each s…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.