Call Now to Set Up Tutoring:

(888) 888-0446

Complex Analysis : Complex Numbers

Study concepts, example questions & explanations for Complex Analysis

Create An Account

All Complex Analysis Resources

1 Diagnostic Test 13 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 Next →

Example Question #1 : Complex Analysis

Evaluate: $\left| 1 - 3 i \right|$

Possible Answers:

$\frac{\sqrt{10}}{2}$

$- \sqrt{10}$

$\sqrt{10}$

Correct answer:

$\sqrt{10}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| 1 - 3 i \right| = \sqrt{ 1 + 9 }$

$= \sqrt{ 10 }$

Report an Error

Example Question #2 : Complex Analysis

Evaluate:

$\left| 9 - 9 i \right|$

Possible Answers:

$- 9 \sqrt{2}$

$9 \sqrt{2}$

$\frac{9 \sqrt{2}}{2}$

162

Correct answer:

$9 \sqrt{2}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| 9 - 9 i \right| = \sqrt{ 81 + 81 }$

$= \sqrt{ 162 }$

$= 9 \sqrt{2}$

Report an Error

Example Question #3 : Complex Analysis

Evaluate:

$\left| 6 - 3 i \right|$

Possible Answers:

$\frac{3 \sqrt{5}}{2}$

$- 3 \sqrt{5}$

$3 \sqrt{5}$

Correct answer:

$3 \sqrt{5}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| 6 - 3 i \right| = \sqrt{ 36 + 9 }$

$= \sqrt{ 45 }$

$= 3 \sqrt{5}$

Report an Error

Example Question #4 : Complex Numbers

Evaluate:

$\left| ( 9 + 7 i ) ( -5 + 6 i ) \right|$

Possible Answers:

$\sqrt{7930}$

$- \sqrt{7930}$

$\frac{\sqrt{7930}}{2}$

7930

Correct answer:

$\sqrt{7930}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| ( 9 + 7 i ) ( -5 + 6 i ) \right| = \sqrt{ 81 + 49 }\cdot \sqrt{ 25 + 36 }$

$= \sqrt{130} \cdot \sqrt{61}$

$= \sqrt{7930}$

Report an Error

Example Question #5 : Complex Numbers

Evaluate:

$\left| ( 9 + 2 i ) ( -9 + 4 i ) \right|$

Possible Answers:

8245

$- \sqrt{8245}$

$\frac{\sqrt{8245}}{2}$

$\sqrt{8245}$

Correct answer:

$\sqrt{8245}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| ( 9 + 2 i ) ( -9 + 4 i ) \right| = \sqrt{ 81 + 4 }\cdot \sqrt{ 81 + 16 }$

$= \sqrt{85} \cdot \sqrt{97}$

$= \sqrt{8245}$

Report an Error

Example Question #6 : Complex Numbers

Evaluate:

$\left| ( 7 + 6 i ) ( -8 + 6 i ) \right|$

Possible Answers:

$5 \sqrt{85}$

$- 10 \sqrt{85}$

$10 \sqrt{85}$

8500

Correct answer:

$10 \sqrt{85}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| ( 7 + 6 i ) ( -8 + 6 i ) \right| = \sqrt{ 49 + 36 }\cdot \sqrt{ 64 + 36 }$

$= \sqrt{85} \cdot 10$

$= 10 \sqrt{85}$

Report an Error

Example Question #7 : Complex Numbers

Evaluate:

$\left| ( 5 + 6 i ) ( -8 + 5 i ) \right|$

Possible Answers:

5429

$\sqrt{5429}$

$- \sqrt{5429}$

$\frac{\sqrt{5429}}{2}$

Correct answer:

$\sqrt{5429}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| ( 5 + 6 i ) ( -8 + 5 i ) \right| = \sqrt{ 25 + 36 }\cdot \sqrt{ 64 + 25 }$

$= \sqrt{61} \cdot \sqrt{89}$

$= \sqrt{5429}$

Report an Error

Example Question #8 : Complex Numbers

Evaluate:

$\left| ( 10 + 3 i ) ( -5 + 4 i ) \right|$

Possible Answers:

$- \sqrt{4469}$

$\sqrt{4469}$

$\frac{\sqrt{4469}}{2}$

4469

Correct answer:

$\sqrt{4469}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| ( 10 + 3 i ) ( -5 + 4 i ) \right| = \sqrt{ 100 + 9 }\cdot \sqrt{ 25 + 16 }$

$= \sqrt{109} \cdot \sqrt{41}$

$= \sqrt{4469}$

Report an Error

Example Question #9 : Complex Numbers

Evaluate:

$\left| ( 9 + i ) ( -9 + 6 i ) \right|$

Possible Answers:

$\frac{3 \sqrt{1066}}{2}$

9594

$- 3 \sqrt{1066}$

$3 \sqrt{1066}$

Correct answer:

$3 \sqrt{1066}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| ( 9 + i ) ( -9 + 6 i ) \right| = \sqrt{ 81 + 1 }\cdot \sqrt{ 81 + 36 }$

$= \sqrt{82} \cdot 3 \sqrt{13}$

$= 3 \sqrt{1066}$

Report an Error

Example Question #10 : Complex Numbers

Evaluate:

$\left| ( 8 + 5 i ) ( -5 + 5 i ) \right|$

Possible Answers:

4450

$- 5 \sqrt{178}$

$5 \sqrt{178}$

$\frac{5 \sqrt{178}}{2}$

Correct answer:

$5 \sqrt{178}$

Explanation:

The general formula to figure out the modulus is

$\left|a+bi\right|=\sqrt{a^2+b^2}$

We apply this to get

$\left| ( 8 + 5 i ) ( -5 + 5 i ) \right| = \sqrt{ 64 + 25 }\cdot \sqrt{ 25 + 25 }$

$= \sqrt{89} \cdot 5 \sqrt{2}$

$=5 \sqrt{178}$

Report an Error

← Previous 1 2 3 Next →

View Tutors

Germaine
Certified Tutor

Princeton University, Bachelor in Arts, Philosophy.

View Tutors

Sakshi
Certified Tutor

M S Ramaiah College of Arts, Science and commerce, Bachelor, Chemistry, Biotechnology, Microbiology .

View Tutors

Tola
Certified Tutor

Indiana University-Bloomington, Bachelor in Arts, Chemistry. Harvard University, Doctor of Medicine, Homeopathic Medicine.

All Complex Analysis Resources

1 Diagnostic Test 13 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Philadelphia, English Tutors in New York City, MCAT Tutors in Boston, Spanish Tutors in Boston, Math Tutors in Chicago, SAT Tutors in Phoenix, Algebra Tutors in Washington DC, ACT Tutors in Washington DC, SAT Tutors in Los Angeles, Algebra Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Chicago, ISEE Courses & Classes in Atlanta, Spanish Courses & Classes in Seattle, ISEE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in San Diego, ACT Courses & Classes in Phoenix, GRE Courses & Classes in Philadelphia, GMAT Courses & Classes in Houston, ISEE Courses & Classes in Boston

Popular Test Prep

GRE Test Prep in Chicago, SSAT Test Prep in Phoenix, SAT Test Prep in Miami, ACT Test Prep in Phoenix, SSAT Test Prep in Chicago, ISEE Test Prep in Phoenix, MCAT Test Prep in Phoenix, LSAT Test Prep in Atlanta, ISEE Test Prep in Los Angeles, SAT Test Prep in New York City

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

Complex Analysis : Complex Numbers

Study concepts, example questions & explanations for Complex Analysis

All Complex Analysis Resources

Example Questions

Example Question #1 : Complex Analysis

Example Question #2 : Complex Analysis

Example Question #3 : Complex Analysis

Example Question #4 : Complex Numbers

Example Question #5 : Complex Numbers

Example Question #6 : Complex Numbers

Example Question #7 : Complex Numbers

Example Question #8 : Complex Numbers

Example Question #9 : Complex Numbers

Example Question #10 : Complex Numbers

All Complex Analysis Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: