Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Mathematical Relationships and Basic Graphs

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 #73 : Imaginary Numbers

What is the value of $i^{42}$ , if $\small i$ = $\small \sqrt{-1}$ ?

Possible Answers:

$\textup{No solution}$

$\small i$

$\small -i$

Correct answer:

Explanation:

We know that $\small i=\sqrt{-1}}$ . Therefore, $\small i^{2}=-1, i^{3}=-\sqrt{-1}, i^{4}=1$ . Thus, every exponent of $\small i$ that is a multiple of 4 will yield the value of $\small 1$ . This makes $\small i^{40} =1$ . Since $\small i^{42}=i^{40}*i*i$ , we know that $\small i^{42}=1*i*i=i^{2}=-1$ .

Report an Error

Example Question #3 : Complex Numbers

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

Possible Answers:

8-6i

7(1-i)

The answer is not present.

7-6i

Correct answer:

8-6i

Explanation:

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

Combine like terms:

7+i-i(7+i)

Distribute:

7+i-7i-i^2

Combine like terms:

7+i-7i-(-1)

$\mathbf{8-6i}$

Report an Error

Example Question #13 : Basic Operations With Complex Numbers

$\sqrt{-4}*\sqrt{-25}*\sqrt{-64}$

Possible Answers:

80i

80i^3

-8i

-80i

Correct answer:

-80i

Explanation:

$\sqrt{-4}*\sqrt{-25}*\sqrt{-64}$

2i*5i*8i=80i^3

i^3=-1

$\mathbf{-80i}$

Report an Error

Example Question #401 : College Algebra

Rationalize the complex fraction: $\frac{2+i}{3-i}$

Possible Answers:

$\frac{5+i}{10}$

$\frac{5+5i}{8}$

$\frac{7+5i}{10}$

$\frac{1+i}{2}$

$\frac{1-i}{2}$

Correct answer:

$\frac{1+i}{2}$

Explanation:

To rationalize a complex fraction, multiply numerator and denominator by the conjugate of the denominator.

$\frac{(2+i)(3+i)}{(3-i)(3+i)}$

$\frac{6+3i+2i+i^2}{9-3i+3i-i^2}$

$\frac{5+5i}{10}$

$\frac{1+i}{2}$

Report an Error

Example Question #401 : College Algebra

Rationalize the complex fraction: $\frac{2+i}{3-i}$

Possible Answers:

$\frac{5+i}{10}$

$\frac{5+5i}{8}$

$\frac{7+5i}{10}$

$\frac{1+i}{2}$

$\frac{1-i}{2}$

Correct answer:

$\frac{1+i}{2}$

Explanation:

To rationalize a complex fraction, multiply numerator and denominator by the conjugate of the denominator.

$\frac{(2+i)(3+i)}{(3-i)(3+i)}$

$\frac{6+3i+2i+i^2}{9-3i+3i-i^2}$

$\frac{5+5i}{10}$

$\frac{1+i}{2}$

Report an Error

Example Question #11 : Basic Operations With Complex Numbers

Multiply: (3i + 1 )(3 - 4i)

Possible Answers:

5i+15

2 - 12i

5i-9

3-7i

Correct answer:

5i+15

Explanation:

Distribute:

3i(3-4i) = 9i + 12

1(3-4i) = 3 - 4i

combine like terms:

5i + 15

Report an Error

Example Question #402 : College Algebra

Multiply: (3+i)(5-4i)

Possible Answers:

11-7i

15-11i

15-3i

19+17i

19-7i

Correct answer:

19-7i

Explanation:

Use FOIL to multiply the two binomials.

Recall that FOIL stands for Firsts, Outers, Inners, and Lasts.

(3+i)(5-4i)

15+5i-12i-4i^2

Remember that i^2=-1

15-7i+4

19-7i

Report an Error

Example Question #12 : Basic Operations With Complex Numbers

Simplify: (5-3i)-(2+2i)

Possible Answers:

7-i

3-5i

3-i

7+i

Correct answer:

3-5i

Explanation:

Distribute the minus sign:

5-3i-2-2i

Combine like terms:

3-5i

Report an Error

Example Question #21 : Basic Operations With Complex Numbers

Simplify:

(3+i)(1-2i)

Possible Answers:

5+5i

1-2i

1-5i

5-5i

3-2i

Correct answer:

5-5i

Explanation:

Use FOIL to multiply the binomials:

3-6i+i-2i^2

Change i^2 to -1:

3-6i+i+2

Combine like terms:

5-5i

Report an Error

Example Question #84 : Imaginary Numbers

Find $i^{123}$

Possible Answers:

Correct answer:

Explanation:

i^1=i

i^2=-1

i^3=-i

i^4=1

This pattern repeats every four powers. Divide the power by 4:

$\frac{123}{4}=30 R3$

Since the remainder is 3, it is equivalent to i^3 , or .

Report an Error

View Algebra 2 Tutors

Hayley
Certified Tutor

University of North Florida, Bachelor in Arts, English.

View Algebra 2 Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Algebra 2 Tutors

Joseph
Certified Tutor

CUNY College of Staten Island, Bachelor in Arts, Applied Psychology. New York University, Master of Arts, Applied Psychology.

All Algebra II Resources

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

Popular Subjects

Spanish Tutors in San Francisco-Bay Area, Calculus Tutors in Boston, Chemistry Tutors in Washington DC, Chemistry Tutors in Denver, Reading Tutors in Philadelphia, Physics Tutors in Phoenix, Calculus Tutors in Phoenix, Math Tutors in Houston, English Tutors in Dallas Fort Worth, ACT Tutors in San Diego

Popular Courses & Classes

SSAT Courses & Classes in New York City, SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Houston, LSAT Courses & Classes in New York City, SAT Courses & Classes in San Diego, SAT Courses & Classes in Washington DC, ISEE Courses & Classes in Denver, MCAT Courses & Classes in Philadelphia, Spanish Courses & Classes in New York City, LSAT Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in San Diego, GRE Test Prep in Washington DC, SAT Test Prep in Denver, GRE Test Prep in Los Angeles, MCAT Test Prep in Los Angeles, GRE Test Prep in Miami, GMAT Test Prep in San Diego, GRE Test Prep in San Diego, ACT Test Prep in San Diego, GMAT Test Prep in Washington DC

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 : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #73 : Imaginary Numbers

Example Question #3 : Complex Numbers

Example Question #13 : Basic Operations With Complex Numbers

Example Question #401 : College Algebra

Example Question #401 : College Algebra

Example Question #11 : Basic Operations With Complex Numbers

Example Question #402 : College Algebra

Example Question #12 : Basic Operations With Complex Numbers

Example Question #21 : Basic Operations With Complex Numbers

Example Question #84 : Imaginary Numbers

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: