💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

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.$$\frac{\frac{1}{5}-\frac{1}{5} i}{\frac{5}{3}-4 i}$$

$=\frac{1}{5} \cdot \frac{7+1}{25}=\frac{7}{125}+\frac{1}{125} i$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Oregon State University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

02:14

In $46-60,$ write each quo…

02:42

02:29

02:22

02:09

01:37

03:10

02:33

01:19

all right, so we want to change this quotient into standard form. And it makes sense to me looking at this numerator that we should start by factoring 1/5 out of the numerator and that will just make our lives so much easier as we move forward. So we have 1/5 times one minus I over three, minus four I. The next step is to multiply by a special form of one. And that would be the congregate of the denominator. So that would be three plus four I over three plus four I. That's because when we multiply congregates, we're just going to get a real number. So what do we have now? We have our 1/5 and we're going to multiply. The numerator is using the foil method and the same with the denominators. So multiplying enumerators. The first we get three for the outside we get for I for the inside we get negative three I and for the last we get negative. Four. I squared and on the bottom, multiplying. The first gives us nine. The insides and outsides cancel. That's what happens with congregates and the last Give us negative 16. I squared, but we want to do now is replaced the I squared with negative one and combine our like terms. So we have 1/5 times three plus I minus four times negative. One over nine minus 16 times. Negative one. Now, let's simplify that. So we have 1/5 times three plus I plus four over nine plus 16. Okay, so now we have 1/5 times seven plus I over 25. Now we can multiply the 1/5 in the 25 we have 11 25th. And we can break this up into the real part and the imaginary part. So the real part will be 7/1 25 plus the imaginary part 11 25th I

View More Answers From This Book

Find Another Textbook

Numerade Educator

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.$$(5-15 i) \div(3-i)…

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.$$(10+5 i) \div(1+2 …

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{\frac{1}{7}+…

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

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.$$(8+4 i) \div(1+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}

In $9-17,$ graph each system and determine the common solution from the grap…

00:37

In $9-14 :$ a. Find the common difference of each arithmetic sequence. b. Wr…

01:28

In $26-37,$ find each product.$$\left(-\frac{1}{8}+\frac{1}{8} i\rig…

01:10

In $3-18,$ write each number in terms of $i$$$\sqrt{-8}$$

02:38

In $18-35,$ find each common solution algebraically. Express irrational root…

01:40

In $9-14$ : a. For each given value of the discriminant of a quadratic equat…

In $3-14$ , use the quadratic formula to find the roots of each equation. Ir…

In $3-8,$ complete the square of the quadratic expression.$$x^{2}-8 …

01:20

a. Sketch the graph of $y=x^{2}+6 x+2$b. From the graph, estimate the ro…

In $26-37,$ find each product.$$(-4-i)(-4+i)$$

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.