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 #2065 : Mathematical Relationships And Basic Graphs

Simplify: i(3-11i)

Possible Answers:

$3i-11i^{2}$

3-11i

11+3i

11-3i

Correct answer:

11+3i

Explanation:

Simplify: i(3-11i)

$First\ distribute\ the\ i--> i(3-11i)=3i-11i^{2}$

$We\ must\ remember\ that\ i^{2}=-1$

$Substitute\ -1\ for\ i^{2}\ to\ get:$

3i-(11)(-1)=3i+11=11+3i

Report an Error

Example Question #2066 : Mathematical Relationships And Basic Graphs

$Simplify: (2-5i)^{2}$

Possible Answers:

$4-25i^{2}$

$4+25i^{2}$

21-20i

Correct answer:

21-20i

Explanation:

$When\ a\ binomial\ is\ squared\ we\ must\ multiply\ it\ by\ itself.$

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

$Double\ distribute\ or\ FOIL\ to\ get:(2-5i)(2-5i)=4-10i-10i+25i^{2}$

$4-10i-10i+25i^{2}=4-20i+25(i^{2})$

$substitute\ (i^2=-1)$

4-20i+25(-1)=4-20i-25=-21-20i

Report an Error

Example Question #112 : Imaginary Numbers

Evaluate: $-2(i^{10}-i^{25})$

Possible Answers:

2+2i

2-2i

2-i

-2-2i

Correct answer:

2+2i

Explanation:

The value of $i=\sqrt{-1}$ . We can rewrite the expression as the product of exponents to simplify.

$-2(i^{10}-i^{25})=-2((i^{2})^5-(i^{5})^{5})$

Identify the values of i^2 and i^5 .

$i^2=i\cdot i=\sqrt{-1} \cdot\sqrt{-1} = -1$

$i^5 = i^2 \cdot i^2 \cdot i = (-1)(-1)i = i$

Replace the values and simplify.

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

The answer is: 2+2i

Report an Error

Example Question #2071 : Mathematical Relationships And Basic Graphs

Solve: (i^2+2i^8)^2

Possible Answers:

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

Correct answer:

Explanation:

Evaluate the inner terms of the imaginary values.

The value of $i=\sqrt{-1}$ .

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

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

The expression becomes:

(-1+2(1))^2 = (-1+2)^2 = (1)^2 =1

The answer is:

Report an Error

Example Question #114 : Imaginary Numbers

Express the following number in the form a+bi , where and are real numbers:

$\frac{17}{4-3i}$

Possible Answers:

$17+\frac{51}{4}i$

$\frac{68}{25}+\frac{51}{25}i$

$\frac{68}{25}-\frac{51}{25}i$

$\frac{68}{7}-\frac{51}{7}i$

Correct answer:

$\frac{68}{25}+\frac{51}{25}i$

Explanation:

Since there is a complex number in the form a+bi in the denominator of the given expression, multiply the numerator and the denominator of the expression by its complex conjugate:

$\frac{17}{4-3i}=(\frac{17}{4-3i})(\frac{4+3i}{4+3i})$

$=\frac{17(4+3i)}{(4-3i)(4+3i)}$

$=\frac{68+51i}{16-9i^2}$

$=\frac{68+51i}{16+9}$

$=\frac{68+51i}{25}$

$=\frac{68}{25}+\frac{51}{25}i$

This number is now expressed in the form a+bi , where $a=\frac{68}{25}$ and $b=\frac{51}{25}$ . Hence, the correct answer is $\frac{68}{25}+\frac{51}{25}i$ .

Report an Error

Example Question #4731 : Algebra Ii

Evaluate: $2i^{243}-i^3$

Possible Answers:

-2i

-3i

Correct answer:

Explanation:

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

$i^3 = i^2\cdot i =(-1)i = -i$

Rewrite the power of 243 as a product of a power of three.

$2i^{243}-i^3 =2(i^{3})^{81}-i^3 =2(-i)^{81}-(-i)$

Simplify the expression.

2(-i)-(-i) = -2i+i = -i

The answer is:

Report an Error

Example Question #4732 : Algebra Ii

Determine the value of: $3i^{1000}$

Possible Answers:

-3i

Correct answer:

Explanation:

In order to determine the exact value of $i^{1000}$ , we will need to rewrite this exponent as a product of exponents.

$i^{1000} =( i^4)^{250}$

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

i^2=-1

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

$( i^4)^{250}= (1)^{250} = 1$

Therefore,

$3i^{1000} = 3(1) =3$

The answer is:

Report an Error

Example Question #2071 : Mathematical Relationships And Basic Graphs

Add: $4i^4-8i^{20}-12i^2$

Possible Answers:

$\textup{The terms are simplified as is.}$

Correct answer:

Explanation:

The expression contain imaginary terms. The values can be simplified.

Recall that:

$i=\sqrt{-1}$

This indicates that:

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

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

Rewrite the expression. For powers higher than the given terms, we can rewrite that power as a product of exponents.

$4i^4-8i^{20}-12i^2 = 4(1)-8(i^4)^5-12(-1)$

4-8(1)^5+12 = 4-8+12 = 8

The answer is:

Report an Error

Example Question #2071 : Mathematical Relationships And Basic Graphs

Evaluate: $2i^2-100i^{100}$

Possible Answers:

-102-i

-2-i

-2i

-100+i

Correct answer:

Explanation:

Write the first few terms of the imaginary powers.

$i=\sqrt{-1}$

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

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

The term with $i^{100}$ can be rewritten as a product of exponents.

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

Re-substitute the values.

$2i^2-100i^{100}= 2(-1)-100(1) = -2-100 = -102$

The answer is:

Report an Error

Example Question #2071 : Mathematical Relationships And Basic Graphs

Evaluate: (2i^4+3)(-i^2-6)(i^6-i^4)

Possible Answers:

$\textup{Cannot be determined.}$

100

Correct answer:

Explanation:

Do not use the FOIL method to simplify these terms. Instead, write out the first few terms of referring to the problem, as well as the value of i^6 .

$i=\sqrt{-1}$

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

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

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

Substitute all the values of the imaginary numbers to the expression.

(2(1)+3)(-(-1)-6)((-1)-(1))

Simplify the terms.

(5)(-5)(-2) = 50

The answer is:

Report an Error

View Algebra 2 Tutors

Maggie
Certified Tutor

Kalamazoo College, Bachelor of Science, Computer Science.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Algebra 2 Tutors

Charles
Certified Tutor

Pacific Intercontinental College, Master's/Graduate, Mathematics.

All Algebra II Resources

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

Popular Subjects

Algebra Tutors in San Diego, Computer Science Tutors in Atlanta, ISEE Tutors in Houston, English Tutors in New York City, Statistics Tutors in Atlanta, ACT Tutors in Los Angeles, SSAT Tutors in Philadelphia, French Tutors in Seattle, English Tutors in Atlanta, English Tutors in Philadelphia

Popular Courses & Classes

ACT Courses & Classes in Seattle, LSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Miami, Spanish Courses & Classes in Washington DC, ISEE Courses & Classes in Los Angeles, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Miami, GMAT Courses & Classes in Atlanta, ISEE Courses & Classes in Atlanta, Spanish Courses & Classes in Los Angeles

Popular Test Prep

LSAT Test Prep in Washington DC, SSAT Test Prep in New York City, SSAT Test Prep in Philadelphia, ISEE Test Prep in New York City, ISEE Test Prep in Phoenix, ACT Test Prep in Miami, GRE Test Prep in Atlanta, GMAT Test Prep in Atlanta, MCAT Test Prep in New York City, LSAT 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 : Basic Operations with Complex Numbers

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2065 : Mathematical Relationships And Basic Graphs

Example Question #2066 : Mathematical Relationships And Basic Graphs

Example Question #112 : Imaginary Numbers

Example Question #2071 : Mathematical Relationships And Basic Graphs

Example Question #114 : Imaginary Numbers

Example Question #4731 : Algebra Ii

Example Question #4732 : Algebra Ii

Example Question #2071 : Mathematical Relationships And Basic Graphs

Example Question #2071 : Mathematical Relationships And Basic Graphs

Example Question #2071 : 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: