We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Imaginary Numbers

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 #4752 : Algebra Ii

Evaluate: $2i^{878}$

Possible Answers:

-2i

$\textup{The answer is not given.}$

Correct answer:

Explanation:

Write the first few powers of the imaginary term.

$i=\sqrt{-1}$

$i^2 = i\cdot i= -1$

Change the higher ordered power by using the power rule of exponents.

$2i^{878} = 2(i^2)^{439}=2(-1)^{439}=2(-1)$

A negative one to an odd power will be negative one.

The answer is:

Report an Error

Example Question #72 : Basic Operations With Complex Numbers

Add $8 +2 i \sqrt{5}$ to its complex conjugate. What is the result?

Possible Answers:

$-4i \sqrt{5}$

$4i \sqrt{5}$

Correct answer:

Explanation:

The complex conjugate of a complex number a+bi is a-bi .

Therefore, the complex conjugate of $8 +2 i \sqrt{5}$ is $8 -2 i \sqrt{5}$ . Add the two:

$\left (8 +2 i \sqrt{5} \right )+\left ( 8 -2 i \sqrt{5} \right )$

Collect real parts and imaginary parts:

$=8+ 8 +2 i \sqrt{5} -2 i \sqrt{5}$

The imaginary parts cancel out:

=8+ 8

=16

Report an Error

Example Question #2091 : Mathematical Relationships And Basic Graphs

Select the complex conjugate of $9 - i \sqrt{5}$ .

Possible Answers:

$\sqrt{5} + 9i$

$-9 +i \sqrt{5}$

$-9 - i \sqrt{5}$

$\sqrt{5} - 9i$

$9 + i \sqrt{5}$

Correct answer:

$9 + i \sqrt{5}$

Explanation:

The complex conjugate of a complex number a-bi is a+bi , so the complex conjugate of $9 - i \sqrt{5}$ is $9 + i \sqrt{5}$ .

Report an Error

Example Question #2092 : Mathematical Relationships And Basic Graphs

Evaluate $i ^{-34}$ .

Possible Answers:

Correct answer:

Explanation:

To raise to the power of a negative integer, first raise to the absolute value of that integer. Therefore, to find $i ^{-34}$ , we need to look at $i^{34}$ .

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Powers of i

$34 \div 2 = 16 \textrm{ R }2$ , so $i^{34}$ can be determined by selecting the power of corresponding to remainder 2. This is .

Since $i^{34} = -1$ , and by definition, $a^{-N} = \frac{1}{a^{N}}$ , it follows that

$i^{-34} = \frac{1}{i^{34} }= \frac{1}{-1} = -1$ .

Report an Error

Example Question #4761 : Algebra Ii

Select the complex conjugate of .

Possible Answers:

-6i

has no complex conjugate.

Correct answer:

-6i

Explanation:

can be restated in standard complex number form as

0+6i .

The complex conjugate of a complex number a+bi is a-bi , so the complex conjugate of 0+6i is 0-6i , which is equal to -6i . Therefore, -6i is the complex conjugate of .

Report an Error

Example Question #82 : Basic Operations With Complex Numbers

Select the complex conjugate of .

Possible Answers:

-9i

9 has no complex conjugate.

Correct answer:

Explanation:

can be restated in standard complex number form as

-9 + 0i .

The complex conjugate of a complex number a+bi is a-bi , so the complex conjugate of -9 + 0i is -9 - 0i , which is also equal to . Therefore, itself is the complex conjugate of .

Report an Error

Example Question #83 : Basic Operations With Complex Numbers

Select the complex conjugate of $2 + \frac{1}{3} i$ .

Possible Answers:

$-2 + \frac{1}{3} i$

$2 - \frac{1}{3} i$

$\frac{1}{3} + 2i$

$\frac{1}{3} - 2i$

$-2 - \frac{1}{3} i$

Correct answer:

$2 - \frac{1}{3} i$

Explanation:

The complex conjugate of a complex number a+bi is a-bi , so the complex conjugate of $2 + \frac{1}{3} i$ is $2 - \frac{1}{3} i$ .

Report an Error

Example Question #84 : Basic Operations With Complex Numbers

Subtract $7 + i \sqrt{17}$ from its complex conjugate. What is the result?

Possible Answers:

$2 i\sqrt{17}$

$-2 i\sqrt{17}$

Correct answer:

$-2 i\sqrt{17}$

Explanation:

The complex conjugate of a complex number a+bi is a-bi .

Therefore, the complex conjugate of $7 + i \sqrt{17}$ is $7 - i \sqrt{17}$ . Subtract the former from the latter:

$\left (7 - i \sqrt{17} \right )-\left ( 7 + i \sqrt{17} \right )$

Collect real parts and imaginary parts:

$= 7 - 7 - i \sqrt{17} - i \sqrt{17}$

The real parts cancel out:

$= - i \sqrt{17} - i \sqrt{17}$

$= -2 i \sqrt{17}$

Report an Error

Example Question #141 : Imaginary Numbers

Evaluate:

$i^{-47}$

Possible Answers:

Correct answer:

Explanation:

In order to raise to the power of a negative integer, first raise to the absolute value of that integer. Therefore, to find $i^{-47}$ , we need to look at $i^{47}$ .

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the following table:

Powers of i

$47 \div 4 = 11 \textrm{ R }3$ , so $i^{47}$ can be determined by selecting the power of corresponding to remainder 3. This is .

Since $i^{47} = -i$ , and by definition, $a^{-N} = \frac{1}{a^{N}}$ , it follows that

$i^{-47} = \frac{1}{i^{47}} = \frac{1}{-i}$

Rationalize the denominator by multiplying by , the complex conjugate:

$i^{-47} = \frac{1}{-i} = \frac{1 \cdot i}{-i \cdot i} = \frac{i}{-i^{1}} = \frac{i}{-(-1)} = \frac{i}{1} = i$

Report an Error

Example Question #85 : Basic Operations With Complex Numbers

Evaluate:

$i^{64}$

Possible Answers:

Correct answer:

Explanation:

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Powers of i

$64 \div 4 = 16\textrm{ R }0$ , so $i^{64}$ can be determined by selecting the power of corresponding to remainder 0. The corresponding power is 1, so $i^{64} = 1$ .

Report an Error

View Algebra 2 Tutors

Dilip
Certified Tutor

University of Calcutta, Bachelor of Science, Physics. Indiana Institute of Technology, Master of Science, Physics.

View Algebra 2 Tutors

Chernyeh
Certified Tutor

Purdue University-Main Campus, Bachelor of Science, Business Administration and Management.

View Algebra 2 Tutors

Jacob
Certified Tutor

Ohio State University-Main Campus, Bachelor of Science, Political Science and Government.

All Algebra II Resources

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

Popular Subjects

Statistics Tutors in Los Angeles, Statistics Tutors in Boston, ISEE Tutors in Seattle, Biology Tutors in San Diego, SAT Tutors in Denver, English Tutors in Denver, MCAT Tutors in Chicago, SAT Tutors in Philadelphia, ISEE Tutors in Chicago, Statistics Tutors in Dallas Fort Worth

Popular Courses & Classes

GRE Courses & Classes in Houston, LSAT Courses & Classes in San Diego, LSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Philadelphia, SAT Courses & Classes in Houston, SSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle, ISEE Courses & Classes in Denver, ISEE Courses & Classes in New York City, GRE Courses & Classes in Los Angeles

Popular Test Prep

ISEE Test Prep in Miami, SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Houston, ACT Test Prep in Philadelphia, ISEE Test Prep in Phoenix, LSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Washington DC, LSAT Test Prep in Los Angeles, MCAT Test Prep in Phoenix, SAT 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 : Imaginary Numbers

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #4752 : Algebra Ii

Example Question #72 : Basic Operations With Complex Numbers

Example Question #2091 : Mathematical Relationships And Basic Graphs

Example Question #2092 : Mathematical Relationships And Basic Graphs

Example Question #4761 : Algebra Ii

Example Question #82 : Basic Operations With Complex Numbers

Example Question #83 : Basic Operations With Complex Numbers

Example Question #84 : Basic Operations With Complex Numbers

Example Question #141 : Imaginary Numbers

Example Question #85 : Basic Operations With Complex Numbers

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: