We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Complex Numbers

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 Next →

Example Question #21 : Complex Numbers

Simplify:

-6+12i+(-2-3i)

Possible Answers:

8+9i

-8+9i

4-6i

4+5i

Correct answer:

-8+9i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

-6+12i+(-2-3i)=-6+12i-2-3i

Combine like terms- combine the real numbers together and the imaginary numbers together:

-6+12i-2-3i=(-6-2)+(12i-3i)

(-6-2)+(12i-3i)=-8+9i

This gives a final answer of -8+9i

Report an Error

Example Question #131 : Review And Other Topics

Simplify:

5-2i+(4-3i)

Possible Answers:

10+5i

9-6i

9-5i

1-5i

Correct answer:

9-5i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

5-2i+(4-3i)=5-2i+4-3i

Combine like terms- combine the real numbers together and the imaginary numbers together:

5-2i+4-3i=(5+4)+(-2i-3i)

(5+4)+(-2i-3i)=9-5i

This gives a final answer of 9-5i

Report an Error

Example Question #23 : Complex Numbers

Simplify:

11+3i+(-2+6i)

Possible Answers:

1+i

-9+9i

9-i

9+9i

Correct answer:

9+9i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

11+3i+(-2+6i)=11+3i-2+6i

Combine like terms- combine the real numbers together and the imaginary numbers together:

11+3i-2+6i=(11-2)+(3i+6i)

(11-2)+(3i+6i)=9+9i

This gives a final answer of 9+9i

Report an Error

Example Question #24 : Complex Numbers

Simplify:

6-5i-(-12-4i)

Possible Answers:

-6-i

9-i

18+9i

18-i

Correct answer:

18-i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

6-5i-(-12-4i)=6-5i+12+4i

Combine like terms- combine the real numbers together and the imaginary numbers together:

6-5i+12+4i=(6+12)+(-5i+4i)

(6+12)+(-5i+4i)=18-i

This gives a final answer of 18-i

Report an Error

Example Question #25 : Complex Numbers

Simplify:

16-3i-(12-2i)

Possible Answers:

4-5i

4+5i

4-i

28-i

Correct answer:

4-i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

16-3i-(12-2i)=16-3i-12+2i

Combine like terms- combine the real numbers together and the imaginary numbers together:

16-3i-12+2i=(16-12)+(-3i+2i)

(16-12)+(-3i+2i)=4-i

This gives a final answer of 4-i

Report an Error

Example Question #26 : Complex Numbers

Rewrite in standard form:

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

Possible Answers:

None of these

$\frac{1}{7}+\frac{i}{7}$

$\frac{2}{7}+\frac{7i}{12}$

$\frac{2}{7}+\frac{12i}{7}$

$\frac{2}{17}+\frac{12i}{17}$

Correct answer:

$\frac{2}{17}+\frac{12i}{17}$

Explanation:

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

Multiply ply by the conjugate:

$\frac{3+3i}{5-3i}\times \frac{5+3i}{5+3i}=\frac{15+9i+15i+9i^2}{25-9i^2}$

Simplify:

$\frac{15+9i+15i+9i^2}{25-9i^2}=\frac{6+24i}{34}\rightarrow \boldsymbol{\frac{6}{34}+\frac{12i}{17}}$

Report an Error

Example Question #21 : Complex Numbers

Rewrite in standard form:

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

Possible Answers:

$\frac{1}{2}-\frac{5}{2}i$

None of these

$\frac{-1}{2}-\frac{5}{2}i$

$\frac{1}{2}+\frac{5}{2}i$

$\frac{-1}{2}+\frac{5}{2}i$

Correct answer:

$\frac{-1}{2}-\frac{5}{2}i$

Explanation:

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

Find a common denominator and subtract.

To do so multiply the numerator and denominator of both fractions by the denominator of the opposite fraction:

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

Combine and simplify:

$\frac{2-2i-3-3i}{1-i^2}\rightarrow \frac{-1-5i}{2}\rightarrow \boldsymbol{\frac{-1}{2}-\frac{5}{2}i}$

Keep in mind

i^2=-1

Report an Error

← Previous 1 2 3 Next →

View College Algebra Tutors

Benjamin
Certified Tutor

Portland State University, Bachelor of Science, Computer Science.

View College Algebra Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

View College Algebra Tutors

Justin
Certified Tutor

Vanderbilt University, Bachelor, Computer Science, Mathematics, & Philosophy.

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Denver, Reading Tutors in San Francisco-Bay Area, Algebra Tutors in Los Angeles, ISEE Tutors in Washington DC, Math Tutors in Boston, SAT Tutors in Miami, English Tutors in Philadelphia, MCAT Tutors in San Francisco-Bay Area, Math Tutors in Dallas Fort Worth, English Tutors in Denver

Popular Courses & Classes

GRE Courses & Classes in Washington DC, SSAT Courses & Classes in San Diego, SSAT Courses & Classes in Washington DC, ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in Atlanta, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Atlanta, Spanish Courses & Classes in Phoenix, Spanish Courses & Classes in San Diego

Popular Test Prep

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

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

College Algebra : Complex Numbers

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #21 : Complex Numbers

Example Question #131 : Review And Other Topics

Example Question #23 : Complex Numbers

Example Question #24 : Complex Numbers

Example Question #25 : Complex Numbers

Example Question #26 : Complex Numbers

Example Question #21 : Complex Numbers

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: