Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math I : Irrational Numbers

Study concepts, example questions & explanations for SAT II Math I

Create An Account

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Imaginary Roots Of Negative Numbers

Simplify:

(2+5i)(-8-i)

Possible Answers:

-11-42i

-18-5i

42+11i

12+6i

Correct answer:

-11-42i

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(2+5i)(-8-i)=-16-2i-40i-5i^2

Remember that $i=\sqrt-1$ , so i^2=-1 .

Substitute in for i^2

-16-2i-40i-5i^2=-16-42i-5(-1)=-16+5-42i=-11-42i

Report an Error

Example Question #3 : Imaginary Roots Of Negative Numbers

Simplify:

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

Possible Answers:

36-8i

12-8i

-8+36i

-36-8i

Correct answer:

-8+36i

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(2+6i)(5+3i)=10+6i+30i+18i^2

Remember that $i=\sqrt-1$ , so i^2=-1 .

Substitute in for i^2

10+6i+30i+18i^2=10+36i+18(-1)=10-18+36i=-8+36i

Report an Error

Example Question #11 : Sat Subject Test In Math I

Simplify:

(2+5i)(2-5i)

Possible Answers:

4-10i

16-5i

Correct answer:

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(2+5i)(2-5i)=4-10i+10i-25i^2

Remember that $i=\sqrt{-1}$ , so i^2=-1 .

Substitute in for i^2 .

4-10i+10i-25i^2=4-25(-1)=4+25=29

Report an Error

Example Question #101 : Classifying Algebraic Functions

Simplify:

$\frac{8-3i}{2-i}$

Possible Answers:

3i+6

$\frac{19+2i}{5}$

10-7i

$\frac{7+2i}{3}$

Correct answer:

$\frac{19+2i}{5}$

Explanation:

To get rid of the fraction, multiply the numerator and denominator by the conjugate of the denominator.

$\frac{8-3i}{2-i}\left(\frac{2+i}{2+i}\right)$

Now, multiply and simplify.

$\frac{8-3i}{2-i}\left(\frac{2+i}{2+i}\right)=\frac{16+8i-6i-3i^2}{4-i^2}$

Remember that i^2=-1

$\frac{16+8i-6i-3i^2}{4-i^2}=\frac{16+2i-3(-1)}{4-(-1)}=\frac{19+2i}{5}$

Report an Error

Example Question #15 : Number Theory

Write in standard form: $\frac{3}{2+4i}$

Possible Answers:

$\frac{6-12i}{20}$

6-12i

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

None of the other answers

$\frac{3}{10}-\frac{3i}{5}$

Correct answer:

$\frac{3}{10}-\frac{3i}{5}$

Explanation:

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

Multiply by the conjugate:

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

$\frac{3(2-4i)}{4-16i^2}$

$\frac{6-12i}{4-16(-1)}$

$\frac{6-12i}{20}=\frac{6}{20}-\frac{12i}{20}=\mathbf{\frac{3}{10}-\frac{3i}{5}}$

Report an Error

Example Question #22 : Algebra Ii

Simplify the expression.

4i^2-6i-7i^2+3i+4

Possible Answers:

None of the other answer choices are correct.

-3i^2-3i+4

-7-3i

7-3i

Correct answer:

7-3i

Explanation:

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

4i^2-6i-7i^2+3i+4

-3i^2-3i+4

Substitute to eliminate $\small i^2$ .

i^2=-1

-3(-1)-3i+4

Simplify.

3-3i+4=7-3i

Report an Error

Example Question #2 : Basic Operations With Complex Numbers

What is the value of (3 + i)(4 + i) ?

Possible Answers:

12 + 8i

11 + 7i

12 + 6i

Correct answer:

11 + 7i

Explanation:

When dealing with imaginary numbers, we multiply by foiling as we do with binomials. When we do this we get the expression below:

(3+i)(4+i)= 12 + 3i + 4i + i^2

Since we know that i^2 = -1 we get 12 + 7i - 1 which gives us 11 + 7i .

Report an Error

Example Question #1 : Basic Operations With Complex Numbers

$\frac{1-7i}{6-2i}=a-i$

Find .

Possible Answers:

0.5

2.5

Correct answer:

0.5

Explanation:

Multiply the numerator and denominator by the numerator's complex conjugate.

$\frac{1-7i}{6-2i}\ast \frac{6+2i}{6+2i}=\frac{20-40i}{40}$

Reduce/simplify.

Report an Error

Example Question #11 : Irrational Numbers

Multiply:

(2+3i)(1-i)

Answer must be in standard form.

Possible Answers:

2+2i

5+i

2-3i

5-i

Correct answer:

5+i

Explanation:

(2+3i)(1-i)

The first step is to distribute which gives us:

$2-2i+3i-3i^{2}$

$2+i-3i^{2}=2+i+3=5+i$

which is in standard form.

Report an Error

Example Question #12 : Basic Operations With Complex Numbers

Evaluate: i(1+i)(2-i)

Possible Answers:

1+3 i

-3+i

1-3i

-1-3i

-1+3i

Correct answer:

-1+3i

Explanation:

Use the FOIL method to simplify. FOIL means to mulitply the first terms together, then multiply the outer terms together, then multiply the inner terms togethers, and lastly, mulitply the last terms together.

i(1+i)(2-i)

=i[(1)(2)+(1)(-i)+(i)(2)+(i)(-i)]

=i[2-i+2i-i^2]

=i[2+i-i^2]

=2i+i^2-i^3

The imaginary is equal to:

$\sqrt{-1}$

Write the terms for $i, i^2, \textup{and } i^3$ .

$i=\sqrt{-1}$

i^2=-1

$i^3=i \times i^2=-\sqrt{-1}=-i$

Replace $i^2 \textup{ and } i^3$ with the appropiate values and simplify.

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

Report an Error

View SAT Subject Test in Mathematics Level 1 Tutors

Chisom
Certified Tutor

Georgia Southern University, Bachelor of Science, Biochemistry. University of Georgia, Current Grad Student, Pharmacy.

View SAT Subject Test in Mathematics Level 1 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View SAT Subject Test in Mathematics Level 1 Tutors

Austyn
Certified Tutor

Morehead State University, Bachelor of Education, Mathematics Teacher Education. Morehead State University, Master of Arts, M...

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in San Francisco-Bay Area, French Tutors in Atlanta, Spanish Tutors in Chicago, Biology Tutors in Phoenix, Physics Tutors in San Diego, ACT Tutors in Houston, Reading Tutors in Houston, MCAT Tutors in Chicago, Reading Tutors in San Diego, Computer Science Tutors in Philadelphia

Popular Courses & Classes

Spanish Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Boston, Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Seattle, Spanish Courses & Classes in Miami, GRE Courses & Classes in Seattle, MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Houston, GRE Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Philadelphia, MCAT Test Prep in Phoenix, GMAT Test Prep in Phoenix, LSAT Test Prep in Washington DC, LSAT Test Prep in Houston, GRE Test Prep in Boston, SAT Test Prep in Washington DC, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle, SAT Test Prep in Chicago

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

SAT II Math I : Irrational Numbers

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #2 : Imaginary Roots Of Negative Numbers

Example Question #3 : Imaginary Roots Of Negative Numbers

Example Question #11 : Sat Subject Test In Math I

Example Question #101 : Classifying Algebraic Functions

Example Question #15 : Number Theory

Example Question #22 : Algebra Ii

Example Question #2 : Basic Operations With Complex Numbers

Example Question #1 : Basic Operations With Complex Numbers

Example Question #11 : Irrational Numbers

Example Question #12 : Basic Operations With Complex Numbers

All SAT II Math I Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: