Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5111 : Algebra Ii

What is the complex conjugate of 5-2i in standard form?

Possible Answers:

-5+2i

2i+5

-2i+5

5+2i

-2i-5

Correct answer:

5+2i

Explanation:

To find a complex conjugate we change the sign of the imaginary part of the number.

To be in standard form the real number should come before the imaginary part of the number

Report an Error

Example Question #57 : Number Theory

Solve the following equation for x. Express your answer with complex numbers.

$3+2x^{2}=-17$

Possible Answers:

$2i\sqrt{5}$ or $-2i\sqrt{5}$

$i\sqrt{10}$ or $-i\sqrt{10}$

$-i\sqrt{10}$

2+5i or 2-5i

$i\sqrt{10}$

Correct answer:

$i\sqrt{10}$ or $-i\sqrt{10}$

Explanation:

$3+2x^{2}=-17$

Our first goal is to isolate the X. So we subtract the 3 on both sides.

$2x^{2}=-20$

Now we divide by 2 on both sides

$x^{2}=-10$

We square root both sides

$x=\pm \sqrt{-10}$

Simplify the radical

$x=\pm i \sqrt{10}$

Report an Error

Example Question #15 : Irrational Numbers

What is the complex conjugate of

$\sqrt{-324}+22$

Possible Answers:

22i+18

22+18i

22i-18

22-18i

-22+18i

Correct answer:

22-18i

Explanation:

The square of 324 is 18. The negative under the radical means that

${\sqrt{-324}}= 18i$

our problem is now 22+18i . The problem asks for the complex conjugate so we make the imaginary part of the number negative. Giving the final answer of

22-18i .

Report an Error

Example Question #16 : Irrational Numbers

Solve the following equation. Express your answer with complex numbers.

(x-7)^2+21 =5

Possible Answers:

7+4i

7+4i or 7-4i

None of the other answers are correct.

11i

Correct answer:

7+4i or 7-4i

Explanation:

(x-7)^2+21 =5

We need to isolate the x. First we subtract 21 on both sides.

(x-7)^2 =-16

We now take the square root of both sides

$x-7 =\sqrt{-16}$

The square root of a negative has an i

$x-7 =\pm 4i$

Now just add the 7 to both sides

$x =7\pm 4i$

Report an Error

Example Question #60 : Number Theory

Simplify

$\frac{5-2i}{5+2i}$

Possible Answers:

$\frac{21}{29}$

$\frac{21-20i}{29}$

$\frac{21-20i}{21}$

$\frac{29-20i}{21}$

Correct answer:

$\frac{21-20i}{29}$

Explanation:

To simplify we need to remove the complex number from the denominator. To do this our first step is to multiply the expression by the complex conjugate of the denominator.

$\frac{5-2i}{5+2i} \cdot \frac{5-2i}{5-2i}$

Multiply the binomials in the numorator and the denominator. You may use the FOIL method.

$\frac{25-10i-10i+4i^{2}}{25+10i-10i-4i^{2}}$

We know that $i^{2}=-1$ so we replace $i^{2}$ with

$\frac{25-10i-10i-4}{25+10i-10i+4}$

Combine like terms

$\frac{21-20i}{29}$

Report an Error

Example Question #61 : Number Theory

Write the following expression in the standard form for a complex number

i(3+7i)(-4+2i)

Possible Answers:

22-26i

-26i+22

22-2i

22+2i

$-12i-22i^{2}+14i^{^{3}}$

Correct answer:

22-26i

Explanation:

i(3+7i)(-4+2i)

Multiply Binomials ( you may use the FOIL method)

$i(-12+6i-28i+14i^{^{2}})$

We know that $i^{2}=-1$ , so we replace $i^{2}$ with

i(-12+6i-28i-14)

combine like terms

i(-26-22i)

Distribute the i

$-26i - 22i^{2}$

We know that $i^{2}=-1$ , so we replace $i^{2}$ with

-26i+22

Swich to standard form

22-26i

Report an Error

Example Question #21 : Irrational Numbers

What is the sum of (7-2i) and -(-4+8i) ?

Possible Answers:

11+6i

3+6i

11-10i

3-2i

28-16i

Correct answer:

11-10i

Explanation:

(7-2i)+-(-4+8i)

Distribute the negative

7-2i+4-8i

Combine like terms

11-10i

Report an Error

Example Question #22 : Irrational Numbers

Add and combine: $\frac{\pi}{e}+\frac{\sqrt2}{\pi}$

Possible Answers:

$\frac{e\pi^2+e\sqrt2}{e\pi}$

$\frac{\sqrt{\pi^2+2e}}{e\pi}$

$\frac{\pi^2+\sqrt2}{\pi}$

$\frac{\pi^2+\sqrt{2e}}{e\pi}$

$\frac{\pi^2+e\sqrt2}{e\pi}$

Correct answer:

$\frac{\pi^2+e\sqrt2}{e\pi}$

Explanation:

To simplify the irrational numbers as a single fraction, we will need a common denominator by multiplying the denominators together.

The term $e\pi$ is the common denominator. Convert the fractions.

$\frac{\pi}{e}+\frac{\sqrt2}{\pi}=\frac{\pi^2}{e\pi}+\frac{e\sqrt2}{e\pi} = \frac{\pi^2+e\sqrt2}{e\pi}$

The answer is: $\frac{\pi^2+e\sqrt2}{e\pi}$

Report an Error

Example Question #23 : Irrational Numbers

Which of the following is considered an irrational number?

Possible Answers:

$\sqrt{144}$

$0.\bar{6}$

$\sqrt{30}$

ln(e)

3.14159

Correct answer:

$\sqrt{30}$

Explanation:

The irrational numbers do not have a representation of a ratio between two numbers. They cannot be expressed by a fraction.

Repeating decimal numbers are not irrational because they can be rewritten as a fraction.

For instance: $0.\bar{3} = \frac{1}{3}$

The number 3.14159 may represent the short version of $\pi$ , but is not irrational, because 3.14159 is a fixed number and be rewritten as a ratio between two numbers.

The answer is: $\sqrt{30}$

Report an Error

Example Question #5112 : Algebra Ii

$What\ is\ the\ complex\ conjugate\ for\ 3-\sqrt{2}\ ?$

Possible Answers:

$9-\sqrt{4}$

$9+\sqrt{4}$

$3+\sqrt{2}$

$3-\sqrt{2}$

Correct answer:

$3+\sqrt{2}$

Explanation:

The complex conjugate for an irrational binomial number with a radical is simply the original with the sign of the radical changed.

$When\ 3-\sqrt{2}\ is\ multipled\ by\ 3+\sqrt{2}\ this\ will\ produce\ a\ rational\ number.$

Report an Error

View Algebra 2 Tutors

Daniel
Certified Tutor

CUNY Bernard M Baruch College, Bachelor of Science, Accounting.

View Algebra 2 Tutors

Iffy
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Engineering, General. University of Maryland-College P...

View Algebra 2 Tutors

Samita
Certified Tutor

University of Houston, Bachelor of Science, Computer Science. University of Houston, Non Degree Bachelors, Biology, General.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Los Angeles, SSAT Tutors in San Diego, LSAT Tutors in Chicago, Biology Tutors in Boston, Math Tutors in Phoenix, French Tutors in Miami, ISEE Tutors in Chicago, Physics Tutors in Denver, SAT Tutors in Atlanta, SAT Tutors in San Diego

Popular Courses & Classes

SAT Courses & Classes in Boston, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in San Diego, ACT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in New York City

Popular Test Prep

LSAT Test Prep in Houston, GMAT Test Prep in San Diego, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in New York City, LSAT Test Prep in Atlanta, SSAT Test Prep in Chicago, GRE Test Prep in Phoenix, MCAT Test Prep in San Diego, MCAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in San Diego

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #5111 : Algebra Ii

Example Question #57 : Number Theory

Example Question #15 : Irrational Numbers

Example Question #16 : Irrational Numbers

Example Question #60 : Number Theory

Example Question #61 : Number Theory

Example Question #21 : Irrational Numbers

Example Question #22 : Irrational Numbers

Example Question #23 : Irrational Numbers

Example Question #5112 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: