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 #1 : Imaginary Numbers

Simplify the radical.

$\sqrt{-250}$ $\displaystyle \sqrt{-250}$

Possible Answers:

$5i\sqrt{10}$ $\displaystyle 5i\sqrt{10}$

$25i\sqrt{10}$ $\displaystyle 25i\sqrt{10}$

No solution

15i $\displaystyle 15i$

Correct answer:

$5i\sqrt{10}$ $\displaystyle 5i\sqrt{10}$

Explanation:

$\sqrt{-250}$ $\displaystyle \sqrt{-250}$

First, factor the term in the radical.

$\displaystyle -250=(-1)(25)(10)$

$\sqrt{-250}=(\sqrt{-1})(\sqrt{25})(\sqrt{10})$ $\displaystyle \sqrt{-250}=(\sqrt{-1})(\sqrt{25})(\sqrt{10})$

Now, we can simplify.

$\sqrt{-1}=i\ \text{and}\ \sqrt{25}=5$ $\displaystyle \sqrt{-1}=i\ \text{and}\ \sqrt{25}=5$

$(\sqrt{-1})(\sqrt{25})(\sqrt{10})=(i)(5)(\sqrt{10})$ $\displaystyle (\sqrt{-1})(\sqrt{25})(\sqrt{10})=(i)(5)(\sqrt{10})$

$5i\sqrt{10}$ $\displaystyle 5i\sqrt{10}$

Report an Error

Example Question #2 : Understanding Imaginary And Complex Numbers

Multiply: $\displaystyle (3 + 2i)(4 - 3 i)$

Possible Answers:

6+ i $\displaystyle 6+ i$

6-i $\displaystyle 6-i$

6 - 17i $\displaystyle 6 - 17i$

18-17i $\displaystyle 18-17i$

18-i $\displaystyle 18-i$

Correct answer:

18-i $\displaystyle 18-i$

Explanation:

FOIL:

$\displaystyle (3 + 2i)(4 - 3 i)$

$= 3 \cdot 4 -3 \cdot 3i + 2i \cdot4 - 2i \cdot3i$ $\displaystyle = 3 \cdot 4 -3 \cdot 3i + 2i \cdot4 - 2i \cdot3i$

$= 12 -9i + 8i - 6i^{2}$ $\displaystyle = 12 -9i + 8i - 6i^{2}$

$\displaystyle = 12 -9i + 8i - 6 (-1)$

$\displaystyle = 12 -9i + 8i +6$

= 18-i $\displaystyle = 18-i$

Report an Error

Example Question #2 : Imaginary Numbers

Multiply: $\displaystyle (5+4i) (5-4i)$

Possible Answers:

25+16i $\displaystyle 25+16i$

$\displaystyle 9$

$\displaystyle -9$

$\displaystyle 41$

25-16i $\displaystyle 25-16i$

Correct answer:

$\displaystyle 41$

Explanation:

Since 5+4i $\displaystyle 5+4i$ and 5-4i $\displaystyle 5-4i$ are conmplex conjugates, they can be multiplied according to the following pattern:

$(5+4i) (5-4i) = 5 ^{2} + 4^{2} = 25 + 16 = 41$ $\displaystyle (5+4i) (5-4i) = 5 ^{2} + 4^{2} = 25 + 16 = 41$

Report an Error

Example Question #1 : Imaginary Numbers

Multiply:

$\left (7 + i \sqrt{2 } \right )\left (7 - i \sqrt{2 } \right )$ $\displaystyle \left (7 + i \sqrt{2 } \right )\left (7 - i \sqrt{2 } \right )$

Possible Answers:

49-2i $\displaystyle 49-2i$

$\displaystyle 47$

$51 - 2i\sqrt{2}$ $\displaystyle 51 - 2i\sqrt{2}$

$\displaystyle 51$

$51 + 2i\sqrt{2}$ $\displaystyle 51 + 2i\sqrt{2}$

Correct answer:

$\displaystyle 51$

Explanation:

Since $7 + i \sqrt{2 }$ $\displaystyle 7 + i \sqrt{2 }$ and $7 - i \sqrt{2 }$ $\displaystyle 7 - i \sqrt{2 }$ are conmplex conjugates, they can be multiplied according to the following pattern:

$\left (7 + i \sqrt{2 } \right )\left (7 - i \sqrt{2 } \right ) = 7^{2} +\left ( \sqrt{2} \right )^{2} = 49 + 2 = 51$ $\displaystyle \left (7 + i \sqrt{2 } \right )\left (7 - i \sqrt{2 } \right ) = 7^{2} +\left ( \sqrt{2} \right )^{2} = 49 + 2 = 51$

Report an Error

Example Question #5 : Understanding Imaginary And Complex Numbers

Evaluate: $i ^{45}$ $\displaystyle i ^{45}$

Possible Answers:

$\displaystyle -45$

45i $\displaystyle 45i$

$\displaystyle i$

$\displaystyle -1$

$\displaystyle 1$

Correct answer:

$\displaystyle i$

Explanation:

$i ^{N}$ $\displaystyle i ^{N}$ can be evaluated by dividing $\displaystyle N$ by 4 and noting the remainder. Since $45 \div 4 = 11 \textrm{ R } 1$ $\displaystyle 45 \div 4 = 11 \textrm{ R } 1$ - that is, since dividing 45 by 4 yields remainder 1:

$i ^{45} = i ^{1} = i$ $\displaystyle i ^{45} = i ^{1} = i$

Report an Error

Example Question #3 : Imaginary Numbers

Evaluate: $(4 + 3i)^{2}$ $\displaystyle (4 + 3i)^{2}$

Possible Answers:

$\displaystyle 13 - 24i$

$\displaystyle 7$

$\displaystyle 25$

7 + 24i $\displaystyle 7 + 24i$

$\displaystyle 19 + 24i$

Correct answer:

7 + 24i $\displaystyle 7 + 24i$

Explanation:

$(4 + 3i)^{2}$ $\displaystyle (4 + 3i)^{2}$

$= 4^{2} + 2 \cdot 4 \cdot 3i +\left ( 3i \right )^{2}$ $\displaystyle = 4^{2} + 2 \cdot 4 \cdot 3i +\left ( 3i \right )^{2}$

$\displaystyle = 16 + 24i + 9 (-1)$

$\displaystyle = 16 + 24i -9$

$\displaystyle = 7 + 24i$

Report an Error

Example Question #4681 : Algebra Ii

What is the absolute value of 4-3i $\displaystyle 4-3i$

Possible Answers:

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\displaystyle 5$

$\displaystyle -4$

$\frac{-4}{3}$ $\displaystyle \frac{-4}{3}$

$\displaystyle 3$

Correct answer:

$\displaystyle 5$

Explanation:

The absolute value is a measure of the distance of a point from the origin. Using the pythagorean distance formula to calculate this distance.

Report an Error

Example Question #1221 : High School Math

Which of the following is equivalent to:

$-4i^{4} ?$ $\displaystyle -4i^{4} ?$

Possible Answers:

$\displaystyle 4$

$\displaystyle 16$

-4i $\displaystyle -4i$

$\displaystyle -4$

$\displaystyle 4i$

Correct answer:

$\displaystyle -4$

Explanation:

Recall that $i^{2} = -1$ $\displaystyle i^{2} = -1$.

Then, we have that $-4(i^{4}) = -4(i^{2})^{2} = -4(-1)^{2} = -4(1) = -4$ $\displaystyle -4(i^{4}) = -4(i^{2})^{2} = -4(-1)^{2} = -4(1) = -4$.

Note that we used the power rule of exponents and the order of operations to simplify the exponent before multiplying by the coefficient.

Report an Error

Example Question #4 : Imaginary Numbers

Simplify the expression.

$\displaystyle 4i^2-6i-7i^2+3i+4$

Possible Answers:

$\displaystyle -10$

-7-3i $\displaystyle -7-3i$

7-3i $\displaystyle 7-3i$

None of the other answer choices are correct.

$\displaystyle -3i^2-3i+4$

Correct answer:

7-3i $\displaystyle 7-3i$

Explanation:

Combine like terms. Treat $\small i$ $\displaystyle \small i$ as if it were any other variable.

$\displaystyle 4i^2-6i-7i^2+3i+4$

$\displaystyle -3i^2-3i+4$

Substitute to eliminate $\small i^2$ $\displaystyle \small i^2$.

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

$\displaystyle -3(-1)-3i+4$

Simplify.

$\displaystyle 3-3i+4=7-3i$

Report an Error

Example Question #5 : Imaginary Numbers

Which of the following is equivalent to $5i^{2}$ $\displaystyle 5i^{2}$ ?

Possible Answers:

$\displaystyle 5i$

None of the other answer choices are correct.

$\displaystyle -5$

$\displaystyle -25$

$\displaystyle 25$

Correct answer:

$\displaystyle -5$

Explanation:

Recall the basic property of imaginary numbers, $i^{2} = -1$ $\displaystyle i^{2} = -1$.

Keeping this in mind, $5i^{2} = 5(-1) = -5$ $\displaystyle 5i^{2} = 5(-1) = -5$.

Report an Error

View Tutors

Susan
Certified Tutor

Washburn University, Juris Doctor, Legal Studies.

View Tutors

Sandra
Certified Tutor

View Tutors

Basia
Certified Tutor

CUNY Brooklyn College, Bachelor in Arts, Early Childhood Education.

All High School Math Resources

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

Popular Subjects

GMAT Tutors in Chicago, Algebra Tutors in Philadelphia, SAT Tutors in Houston, ACT Tutors in Atlanta, Algebra Tutors in New York City, GMAT Tutors in New York City, MCAT Tutors in Washington DC, Math Tutors in Chicago, Algebra Tutors in Phoenix, Spanish Tutors in Washington DC

Popular Courses & Classes

GMAT Courses & Classes in San Diego, ACT Courses & Classes in Seattle, MCAT Courses & Classes in Chicago, SAT Courses & Classes in Denver, ACT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Phoenix, GRE Courses & Classes in Washington DC, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Denver

Popular Test Prep

SSAT Test Prep in Houston, MCAT Test Prep in San Diego, ACT Test Prep in Seattle, ACT Test Prep in San Diego, GRE Test Prep in Denver, GRE Test Prep in New York City, LSAT Test Prep in Phoenix, SAT Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, GRE Test Prep in Washington DC

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 #1 : Imaginary Numbers

Example Question #2 : Understanding Imaginary And Complex Numbers

Example Question #2 : Imaginary Numbers

Example Question #1 : Imaginary Numbers

Example Question #5 : Understanding Imaginary And Complex Numbers

Example Question #3 : Imaginary Numbers

Example Question #4681 : Algebra Ii

Example Question #1221 : High School Math

Example Question #4 : Imaginary Numbers

Example Question #5 : Imaginary Numbers

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: