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

← Previous 1 2 3 4 5 6 7 8 9 10 … 16 17 Next →

Example Question #51 : Complex Imaginary Numbers

Simplify: $\frac{i^5}{4}*\frac{16}{i^7}$

Possible Answers:

-4i

16i

Correct answer:

Explanation:

We know that $i=\sqrt{-1}$ and i^2=-1 . $\frac{i^5}{4}*\frac{16}{i^7}$ simplifies to $\frac{4}{i^2}$ . Since i^2=-1 our final answer is $\frac{4}{-1}=-4$ .

Report an Error

Example Question #51 : Complex Imaginary Numbers

Simplify: $\frac{1}{4+i}$

Possible Answers:

$\frac{16}{4-i}$

$\frac{16}{4+i}$

$\frac{4-i}{17}$

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

$\frac{4-i}{15}$

Correct answer:

$\frac{4-i}{17}$

Explanation:

To get rid of a complex number, we multiply by the conjugate which is opposite the sign.

$\frac{1}{4+i}=\frac{1}{4+i}*\frac{4-i}{4-i}=\frac{4-i}{16-i^2}=\frac{4-i}{16-(-1)}=\frac{4-i}{17}$

Report an Error

Example Question #52 : Complex Imaginary Numbers

Simplify: $\frac{2-i}{3+i}$

Possible Answers:

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

$\frac{7+i}{8}$

$\frac{7-i}{10}$

$\frac{6-i}{10}$

$\frac{7-i}{8}$

Correct answer:

$\frac{7-i}{10}$

Explanation:

To get rid of a complex number, we multiply by the conjugate which is opposite the sign.

$\frac{2-i}{3+i}=\frac{2-i}{3+i}*\frac{3-i}{3-i}=\frac{6+2i-3i-i^2}{9-i^2}=\frac{6-i-(-1)}{9-(-1)}=\frac{7-i}{10}$

Report an Error

Example Question #54 : Complex Imaginary Numbers

Simplify: $\frac{i^{150}-2i^{8}}{3i^{100}-6}$

Possible Answers:

2i-2

$\frac{1}{9}$

$\textup{The expression cannot be factored.}$

Correct answer:

Explanation:

Write out some of the imaginary terms.

$i=\sqrt{-1}$

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

$i^4 = i^2\cdot i^2 = (-1)\cdot (-1) = 1$

The powers of the imaginary number can be rewritten using the product of exponents.

$i^{150} = (i^2)^{75} = (-1)^{75} = -1$

i^8= (i^4)^2 = (1)^2 =1

$i^{100} = (i^4)^{25} = (1)^{25} = 1$

Replace all the terms back into the expression.

$\frac{i^{150}-2i^{8}}{3i^{100}-6} = \frac{-1-2(1)}{3(1)-6} = \frac{-3}{-3} = 1$

The answer is:

Report an Error

Example Question #55 : Complex Imaginary Numbers

Evaluate: $\frac{i^6+1}{i-1}$

Possible Answers:

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

Correct answer:

Explanation:

The imaginary term is equivalent to $\sqrt{-1}$ .

This means that:

i^6 =( i^2)^3 = (-1)^3 = -1

Substitute this term back into the numerator.

$\frac{i^6+1}{i-1}=\frac{-1+1}{i-1} = \frac{0}{i-1} =0$

There is no need to use extra steps such as multiplying by the conjugate of the denominator to simplify.

The answer is:

Report an Error

Example Question #56 : Complex Imaginary Numbers

Solve: $\frac{2(2i^2-3)}{i^4-i^{12}}$

Possible Answers:

$-\frac{2}{5}i-\frac{4}{5}$

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

$\frac{3}{5}i+\frac{1}{5}$

$-\frac{1}{2}i-5$

-3i-4

Correct answer:

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

Explanation:

Evaluate by first evaluating the imaginary terms.

$i=\sqrt{-1}$

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

$i^4= i^2\cdot i^2 =1$

We can also use the product rule of exponents to simplify the higher powered imaginary numbers.

$i^{12} = (i^4)^3=(1)^3 =1$

$\frac{2(2i^2-3)}{i^4-i^{12}}=\frac{2(2(-1)-3)}{1-1} =\frac{ -10}{0}$

Note that evaluating the denominator will give us a zero denominator.

This will indicate that the expression will approach to infinity.

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

Report an Error

Example Question #57 : Complex Imaginary Numbers

Simplify: $\frac{i^{60}-1}{i^3-1}$

Possible Answers:

i-1

$\textup{Undefined.}$

i+1

Correct answer:

Explanation:

Write the first few terms of the imaginary term.

$i=\sqrt{-1}$

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

$i^3 = i^2\cdot i = -i$

$i^4 = i^2\cdot i^2=1$

i^5 = (i^4)(i)=i

Notice that these terms will be in a pattern for higher order imaginary terms.

Rewrite the numerator using the product of exponents.

$\frac{i^{60}-1}{i^3-1} =\frac{(i^4)^{15}-1}{i^3-1} = \frac{1-1}{-i-1} = 0$

The answer is:

Report an Error

Example Question #58 : Complex Imaginary Numbers

Evaluate: $(7i^{-400})^{3}$

Possible Answers:

$\frac{1}{343}i$

343i

$\frac{1}{343i}$

343

-343i

Correct answer:

343

Explanation:

Using the exponential property, we can expand the term in parentheses by multiplying the inner and outer powers together.

$(7i^{-400})^{3} = (7^3\cdot i^{-400\times 3}) = 7^3 \cdot i^{-1200} = 343 \cdot i^{-1200}$

Evaluate $i^{-1200}$ by breaking this up as a product of imaginary powers.

$i=\sqrt{-1}$

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

$i^4 =i^2\cdot i^2 =1$

$i^{-1200} = (i^4)^{-300} = (1)^{-300} = 1$

This means that:

$343 \cdot i^{-1200}= 343 \cdot 1$

The answer is: 343

Report an Error

Example Question #59 : Complex Imaginary Numbers

Evaluate: $\frac{5i}{6-2i}$

Possible Answers:

$\frac{3}{10}i-\frac{1}{10}$

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

$\frac{7}{10}i-\frac{9}{10}$

$\frac{1}{4}i-\frac{1}{2}$

$\frac{1}{4}i+\frac{5}{2}$

Correct answer:

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

Explanation:

Multiply the top and bottom by the conjugate of the denominator.

$\frac{5i}{6-2i}\cdot \frac{6+2i}{6+2i}$

Simplify the bottom using the FOIL method.

(6)(6)+(6)(2i)+(-2i)(6)+(-2i)(2i)

Simplify the expression by distributing all terms. Recall that $i=\sqrt{-1}$ and i^2=-1 . Replace the term.

36-4i^2 = 36-4(-1) = 36+4 =40

Simplify the top.

5i(6+2i)=30i+10i^2 = 30i+(10)(-1) = 30i-10

Divide this by forty.

$\frac{30i-10}{40} = \frac{3}{4}i-\frac{1}{4}$

The answer is: $\frac{3}{4}i-\frac{1}{4}$

Report an Error

Example Question #60 : Complex Imaginary Numbers

Evaluate: $\frac{2i}{5-2i}$

Possible Answers:

$\frac{10i-4}{29}$

$\frac{10i-4}{21}$

$\frac{10i+4}{29}$

$\frac{10i-4}{5}$

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

Correct answer:

$\frac{10i-4}{29}$

Explanation:

Multiply the top and bottom by the conjugate of the denominator.

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

Distribute the numerator and FOIL the denominator.

$\frac{2i}{5-2i}\cdot \frac{5+2i}{5+2i} = \frac{10i+4i^2}{25-4i^2}$

Recall that $i=\sqrt{-1}$ . This means that $i^2 = i\cdot i = -1$ .

Replace the terms.

$\frac{10i+4(-1)}{25-4(-1)} = \frac{10i-4}{29}$

The answer is: $\frac{10i-4}{29}$

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 … 16 17 Next →

View Algebra 2 Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Algebra 2 Tutors

Humaira
Certified Tutor

North South University, Bachelor of Science, Computer Science.

View Algebra 2 Tutors

Swagatika
Certified Tutor

Regional Institute of Education Bhubaneswar, Bachelor of Economics, Mathematics.

All Algebra II Resources

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

Popular Subjects

Chemistry Tutors in Miami, Chemistry Tutors in Chicago, French Tutors in Dallas Fort Worth, ISEE Tutors in Houston, Spanish Tutors in San Diego, ISEE Tutors in San Diego, GMAT Tutors in Washington DC, SAT Tutors in Phoenix, English Tutors in Philadelphia, Computer Science Tutors in Washington DC

Popular Courses & Classes

GRE Courses & Classes in Phoenix, Spanish Courses & Classes in Houston, GRE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Atlanta, GRE Courses & Classes in Seattle, SSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Los Angeles, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Houston

Popular Test Prep

MCAT Test Prep in San Diego, ISEE Test Prep in Philadelphia, ISEE Test Prep in Boston, GRE Test Prep in San Diego, SSAT Test Prep in Miami, GRE Test Prep in Los Angeles, SSAT Test Prep in Boston, LSAT Test Prep in Boston, GMAT Test Prep in Houston, GMAT Test Prep in Miami

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 #51 : Complex Imaginary Numbers

Example Question #51 : Complex Imaginary Numbers

Example Question #52 : Complex Imaginary Numbers

Example Question #54 : Complex Imaginary Numbers

Example Question #55 : Complex Imaginary Numbers

Example Question #56 : Complex Imaginary Numbers

Example Question #57 : Complex Imaginary Numbers

Example Question #58 : Complex Imaginary Numbers

Example Question #59 : Complex Imaginary Numbers

Example Question #60 : Complex Imaginary Numbers

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: