We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Algebra II

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

$(\sqrt{-6})(\sqrt{-4})(\sqrt{-3})$

Possible Answers:

$-6i\sqrt{2}$

$-4i\sqrt{3}$

$-6i\sqrt{3}$

$-6i\sqrt{5}$

$-4i\sqrt{2}$

Correct answer:

$-6i\sqrt{2}$

Explanation:

Begin by simplifying the radicals using complex numbers:

$(\sqrt{-6})(\sqrt{-4})(\sqrt{-3})$

$=(i\sqrt{6})(2i)(i\sqrt{3})$

Multiply the factors:

$=(2i^2\sqrt{6})(i\sqrt{3})$

$=(2i^3\sqrt{18})$

Simplify. Remember that i^3 is equivalent to .

$=-2i\sqrt{18}$

$=-6i\sqrt{2}$

Report an Error

Example Question #41 : Algebra Ii

Simplify the following complex number expression:

(3i^3)(2i)^2

Possible Answers:

12i

10i

11i

Correct answer:

12i

Explanation:

Begin by completing the square:

(3i^3)(2i)^2

=(3i^3)(4i^2)

Multiply the factors:

=(12i^5)

Simplify. Remember that i^5 is equivalent to .

=12i

Report an Error

Example Question #12 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

(-2i)^4(-4i^3)

Possible Answers:

80i

36i

72i

12i

64i

Correct answer:

64i

Explanation:

Begin by completing the square:

(-2i)^4(-4i^3)

=(16i^4)(-4i^3)

Now, multiply the factors:

=(16i^4)(-4i^3)

=(-64i^7)

Simplify. Remember that i^7 is equivalent to .

=64i

Report an Error

Example Question #13 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

(7+2i)(5-3i)

Possible Answers:

42-12i

44-14i

43-13i

40-10i

41-11i

Correct answer:

41-11i

Explanation:

Use the FOIL (First, Outer, Inner, Last) to multiply the complex numbers:

(7+2i)(5-3i)

=35-21i+10i-6i^2

Combine like terms and simplify. Remember that i^2 is equivalent to .

=35-11i-6i^2

=35-11i+6

=41-11i

Report an Error

Example Question #41 : Algebra Ii

Simplify the following complex number expression:

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

Possible Answers:

$\frac{-4+11i}{5}$

$\frac{-2+11i}{3}$

$\frac{-2+11i}{4}$

$\frac{-2+11i}{5}$

$\frac{-3+11i}{5}$

Correct answer:

$\frac{-2+11i}{5}$

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

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

$=\frac{4+8i+3i+6i^2}{1-4i^2}$

Combine like terms:

$=\frac{4+11i+6i^2}{1-4i^2}$

Simplify. Remember that i^2 is equivalent to .

$=\frac{4+11i-6}{1+4}$

$=\frac{-2+11i}{5}$

Report an Error

Example Question #12 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

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

Possible Answers:

-i^2

i^3

i^2

Correct answer:

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

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

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

Combine like terms:

$=\frac{4-8i+4i^2}{4-4i^2}$

Simplify. Remember that i^2 is equivalent to .

$=\frac{4-8i-4}{4+4}$

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

=-i

Report an Error

Example Question #12 : Using Expressions With Complex Numbers

Simplify the following expression:

(5 + 3i) + (2 - 6i)

Possible Answers:

3 - 3i

7 + 9i

7 + 3i

7 - 3i

7 - 9i

Correct answer:

7 - 3i

Explanation:

Simplifying expressions with complex numbers uses exactly the same process as simplifying expressings with one variable. In this case, behaves similarly to any other variable. Thus, we have:

(5 + 3i) + (2 - 6i) = (5 +2) + (3 - 6)i = 7 - 3i

Report an Error

Example Question #13 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

(3+8i)(3-8i)

Possible Answers:

Correct answer:

Explanation:

Use the FOIL (First, Outer, Inner, Last) method to expand the expression:

(3+8i)(3-8i)

=9-24i+24i-64i^2

=9-64i^2

Simplify. Remember that i^2 is equivalent to .

=9+64

=73

Report an Error

Example Question #1 : Understanding Square Roots

Simplify the expression. Find the positive solution only.

$\sqrt{50x^3y^4}$

Possible Answers:

25xy

$xy^2\sqrt{50xy^2}$

$5xy^2\sqrt{2x}$

$25x^2y^4\sqrt{2x}$

$5xy\sqrt{2x}$

Correct answer:

$5xy^2\sqrt{2x}$

Explanation:

When working in square roots, each component can be treated separately.

$\sqrt{50x^3y^4}=\sqrt{50}\sqrt{x^3}\sqrt{y^4}$

Now, we can simplify each term.

$\sqrt{50}=5\sqrt{2}$

$\sqrt{x^3}=x\sqrt{x}$

$\sqrt{y^4}=y^2$

Combine the simplified terms to find the answer. Anything outside of the square root is combined, while anything under the root is combined under the root.

$(5\sqrt{2})(x\sqrt{x})(y^2)=5xy^2\sqrt{2x}$

Report an Error

Example Question #1 : Understanding Radicals

Convert the radical to exponential notation.

$\small \sqrt[4]{13}$

Possible Answers:

$\small 13^4$

$\small 169$

$\small \sqrt{13^4}$

$13^{\frac{1}{4}}$

Correct answer:

$13^{\frac{1}{4}}$

Explanation:

Remember that any term outside the radical will be in the denominator of the exponent.

$\sqrt[b]{x^a}=x^{\frac{a}{b}}$

Since does not have any roots, we are simply raising it to the one-fourth power.

$\sqrt[4]{13}=13^{\frac{1}{4}}$

Report an Error

View Tutors

Paarth
Certified Tutor

New Jersey Institute of Technology, Bachelor of Science, Computer Science.

View Tutors

Joshua
Certified Tutor

Murray State University, Bachelor in Arts, Spanish. Lipscomb University, Bachelor of Science, Teacher Assistant.

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Dallas Fort Worth, GRE Tutors in Phoenix, Algebra Tutors in Chicago, ISEE Tutors in Boston, Chemistry Tutors in San Francisco-Bay Area, MCAT Tutors in Dallas Fort Worth, Calculus Tutors in Miami, ISEE Tutors in Philadelphia, ISEE Tutors in San Diego, GRE Tutors in Seattle

Popular Courses & Classes

ISEE Courses & Classes in Seattle, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Boston, SAT Courses & Classes in New York City, LSAT Courses & Classes in New York City, SAT Courses & Classes in Chicago, MCAT Courses & Classes in Seattle, LSAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

ACT Test Prep in Dallas Fort Worth, LSAT Test Prep in Los Angeles, GRE Test Prep in New York City, SAT Test Prep in New York City, LSAT Test Prep in Boston, ACT Test Prep in Washington DC, ISEE Test Prep in Phoenix, GMAT Test Prep in Seattle, GRE Test Prep in San Francisco-Bay Area, LSAT Test Prep in San Francisco-Bay Area

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

High School Math : Algebra II

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : Using Expressions With Complex Numbers

Example Question #41 : Algebra Ii

Example Question #12 : Using Expressions With Complex Numbers

Example Question #13 : Using Expressions With Complex Numbers

Example Question #41 : Algebra Ii

Example Question #12 : Using Expressions With Complex Numbers

Example Question #12 : Using Expressions With Complex Numbers

Example Question #13 : Using Expressions With Complex Numbers

Example Question #1 : Understanding Square Roots

Example Question #1 : Understanding Radicals

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: