Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Basic Operations with Complex 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 #2089 : Mathematical Relationships And Basic Graphs

Simplify: $\frac{2}{i^4}+\frac{i^2}{3}-2$

Possible Answers:

$\frac{1}{3}$

i-2

2-i

$-\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

Simplify each term. Recall that $i=\sqrt{-1}$ .

$\frac{2}{i^4}+\frac{i^2}{3}-2 = \frac{2}{1}+\frac{-1}{3}-2$

Simplify the expression.

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

Report an Error

Example Question #131 : Imaginary Numbers

Solve: -6i^2+30i^2-2i^2

Possible Answers:

Correct answer:

Explanation:

Rewrite the terms with the actual value of the imaginary term.

Recall that $i=\sqrt{-1}$ .

This means that: i^2 =-1

Replace this for all the terms.

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

-6(-1)+30(-1)-2(-1) = -22

The answer is:

Report an Error

Example Question #4751 : Algebra Ii

Evaluate: $-2i^{5000}$

Possible Answers:

-2-i

Correct answer:

Explanation:

Write the first few values of the imaginary term .

$i=\sqrt{-1}$

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

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

Rewrite the expression using the product of exponents.

$-2i^{5000} = -2(i^4)^{1250}= -2(1)^{1250}$

The value of one to this power will remain the same.

-2(1) =-2

The answer is:

Report an Error

Example Question #2092 : Mathematical Relationships And Basic Graphs

Compute: 2i^2+3i^4-4i^6-5i^2

Possible Answers:

Correct answer:

Explanation:

To be able to evaluate the expression, we will need to write out the value of the imaginary terms.

Recall that: $i=\sqrt{-1}$

i^2= -1

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

$i^6 = i^4 \cdot i^2 = (1) \cdot (-1) = -1$

Replace the terms.

2i^2+3i^4-4i^6-5i^2= 2(-1)+3(1)-4(-1)-5(-1)

=-2+3+4+5 = 10

The answer is:

Report an Error

Example Question #4751 : Algebra Ii

Evaluate: (3+2i)^3

Possible Answers:

54-9i

9-46i

54i-9

46i-9

Correct answer:

46i-9

Explanation:

Rewrite the problem as separate groups of binomials.

(3+2i)^3=(3+2i)(3+2i)(3+2i)

Use the FOIL method to expand the first two terms.

(3+2i)(3+2i) = (3)(3)+(3)(2i)+(2i)(3)+(2i)(2i)

Simplify the right side.

9+12i+4i^2

Recall that since $i=\sqrt{-1}$ , the value of $i^2 = i\cdot i =-1$ .

9+12i+4(-1) = 12i+5

Multiply this value with the third binomial.

(12i+5)(3+2i) = (12i)(3)+(12i)(2i)+(5)(3)+(5)(2i)

Simplify the terms.

36i+24i^2+15+10i=36i+24(-1)+15+10i = 46i-9

The answer is: 46i-9

Report an Error

Example Question #4752 : Algebra Ii

Solve: $\frac{-2i^3}{i^{-7}}-i^2$

Possible Answers:

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

Correct answer:

Explanation:

In order to solve this expression, we will need to evaluate each term.

Use the property of exponents to subtract the powers in the fraction.

$\frac{-2i^3}{i^{-7}} = -2i^{3-(-7)} = -2i^{10}$

This term can be written as a fraction.

$-2i^{-10} = -2\cdot \frac{1}{i^{10}}$

Recall that the imaginary term $i=\sqrt{-1}$ . This means that:

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

$i^{10} = (i^2)^5 = (-1)^5 = -1$

Replace the terms.

$-2\cdot \frac{1}{i^{10}} = -2\cdot \frac{1}{-1} = 2$

Solve the expression by replacing the values in the original expression.

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

The answer is:

Report an Error

Example Question #4753 : Algebra Ii

Simplify: $-1000i^{52}+ 500i^{30}$

Possible Answers:

1000-500i

1000+500i

-500i

Correct answer:

Explanation:

Write the first few powers of the imaginary term.

$i=\sqrt{-1}$

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

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

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

We can then rewrite the higher powered imaginary terms by the product of exponents.

$-1000i^{52}+ 500i^{30} = -1000(i^4)^{13}+500(i^2)^{15}$

Simplify the terms.

$-1000(1)^{13}+500(-1)^{15} = -1000-500 = -1500$

The answer is:

Report an Error

Example Question #2096 : Mathematical Relationships And Basic Graphs

Compute: $-5i^{1234}$

Possible Answers:

-5-i

-5i

Correct answer:

Explanation:

Identify the first two powers of the imaginary term.

$i=\sqrt{-1}$

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

Rewrite the expression as a product of exponents.

$-5i^{1234}=-5(i^{2})^{617} = -5(-1)^{617}$

Negative one to an odd power will be negative one.

-5(-1) =5

The answer is:

Report an Error

Example Question #2097 : Mathematical Relationships And Basic Graphs

Evaluate: $2i^{878}$

Possible Answers:

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

-2i

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 #2098 : Mathematical Relationships And Basic Graphs

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

View Algebra 2 Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Algebra 2 Tutors

Allison
Certified Tutor

Asbury University, Bachelor of Education, Mathematics Teacher Education.

View Algebra 2 Tutors

Andrew
Certified Tutor

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

All Algebra II Resources

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

Popular Subjects

Computer Science Tutors in San Diego, English Tutors in New York City, French Tutors in San Diego, Physics Tutors in Miami, ISEE Tutors in Atlanta, Physics Tutors in Seattle, Algebra Tutors in San Diego, SAT Tutors in Philadelphia, Chemistry Tutors in Los Angeles, Physics Tutors in Houston

Popular Courses & Classes

GRE Courses & Classes in Denver, SSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Boston, SSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Washington DC, MCAT Courses & Classes in Miami, Spanish Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Miami, SSAT Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Washington DC, ISEE Test Prep in Atlanta, SSAT Test Prep in Miami, GMAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Dallas Fort Worth, GRE Test Prep in Los Angeles, ISEE Test Prep in Boston, ACT Test Prep in Boston, ACT Test Prep in Dallas Fort Worth

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 : Basic Operations with Complex Numbers

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2089 : Mathematical Relationships And Basic Graphs

Example Question #131 : Imaginary Numbers

Example Question #4751 : Algebra Ii

Example Question #2092 : Mathematical Relationships And Basic Graphs

Example Question #4751 : Algebra Ii

Example Question #4752 : Algebra Ii

Example Question #4753 : Algebra Ii

Example Question #2096 : Mathematical Relationships And Basic Graphs

Example Question #2097 : Mathematical Relationships And Basic Graphs

Example Question #2098 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: