Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Complex Numbers

Study concepts, example questions & explanations for Trigonometry

Create An Account

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Complex Numbers

Name the real part of this expression and the imaginary part of this expression: 3-7i .

Possible Answers:

Real:

Imaginary:

All parts are imaginary; there are no real parts

Real:

Imaginary: -7i

Real:

Imaginary:

All parts are real; there are no imaginary parts

Correct answer:

Real:

Imaginary: -7i

Explanation:

The real part of this expression includes any terms that do not have attached to them. Therefore the real part of this expression is 3. The imaginary part of this expression includes any terms with that cannot be further reduced; the imaginary part of this expression is -7i .

Report an Error

Example Question #1 : Complex Numbers

Find the product of the complex number and its conjugate:

4+2i

Possible Answers:

12+16i

4-2i

Correct answer:

Explanation:

To solve this problem, we must first identify the conjugate of this complex number. The conjugate keeps the real portion of the number the same, but changes the sign of the imaginary part of the number. Therefore the conjugate of 4+2i is 4-2i . Now, we need to multiply these together using distribution, combining like terms, and substituting i^2=-1 .

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

$16-8i+8i-4i^{2}$

16+4

Report an Error

Example Question #3 : Complex Numbers

What is the complex conjugate of $\sqrt{3}-22i$ ?

Possible Answers:

-22i

$\sqrt{3}+22i$

$\sqrt{3-22i}$

$\sqrt{3}-22i$

$\sqrt{3+22i}$

Correct answer:

$\sqrt{3}+22i$

Explanation:

To solve this problem, we must understand what a complex conjugate is and how it relates to a complex number. The conjugate of a number a+bi is a-bi . Therefore the conjugate of $\sqrt{3}-22i$ is $\sqrt{3}+22i$ .

Report an Error

Example Question #1 : Complex Numbers

Simplify $\left ( 6+20i \right )+\left ( 8+10i \right )$ .

Possible Answers:

15+20i

28+16i

44i

14+30i

Correct answer:

14+30i

Explanation:

To add complex numbers, we must combine like terms: real with real, and imaginary with imaginary.

$\left ( 6+20i \right )+\left ( 8+10i \right )$

=(6+8)+(20i+10i)

=14+30i

Report an Error

Example Question #2 : Complex Numbers

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

Possible Answers:

4+8i

4+2i

8+8i

12i

Correct answer:

4+8i

Explanation:

In order to solve this problem, we must combine real numbers with real numbers and imaginary numbers with imaginary numbers. Be careful to distribute the subtraction sign to all terms in the second set of parentheses.

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

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

=4+8i

Report an Error

Example Question #5 : Complex Numbers

Simplify $\left ( 4+5i \right )^{2}$ .

Possible Answers:

16+25i^2

16+40i+25i^2

9+40i

-9+40i

Correct answer:

-9+40i

Explanation:

To solve this problem, make sure you set it up to multiply the entire parentheses by itself (a common mistake it to try to simply distribute the exponent 2 to each of the terms in the parentheses.)

$\left ( 4+5i \right )^{2}$

$\left ( 4+5i \right )\left ( 4+5i \right )$

$16+20i+20i+25i^{2}$

16+40i-25 (recall that i^2=-1 )

-9+40i

Please note that while the answer choice 16+40i+25i^2 is not incorrect, it is not fully simplified and therefore not the correct choice.

Report an Error

Example Question #6 : Complex Numbers

What is the complex conjugate of 5? What is the complex conjugate of 3i?

Possible Answers:

Complex conjugates do not exist for these terms

5; 3i

5; -3i

-5; -3i

-5; 3i

Correct answer:

5; -3i

Explanation:

While these terms may not look like they follow the typical format of a+bi , don't let them fool you! We can read 5 as 5+0i and we can read 3i as 0+3i . Now recalling that the complex conjugate of a+bi is a-bi , we can see that the complex conjugate of is just and the complex conjugate of is -3i

Report an Error

Example Question #7 : Complex Numbers

Perform division on the following expression by utilizing a complex conjugate:

$\frac{3+2i}{9-6i}$

Possible Answers:

$\frac{5+12i}{39}$

-6+8i

9+6i

$\frac{13+12i}{39}$

Correct answer:

$\frac{5+12i}{39}$

Explanation:

To perform division on complex numbers, multiple both the numerator and the denominator of the fraction by the complex conjugate of the denominator. This looks like:

$\frac{3+2i}{9-6i}\cdot \frac{9+6i}{9+6i}$

$=\frac{\left ( 3+2i \right )\left ( 9+6i \right )}{\left ( 9-6i \right )\left ( 9+6i \right )}$

$=\frac{27+18i+18i+12i^{2}}{81+54i-54i-36i^{2}}$

$=\frac{27+36i-12}{81+36}$

$=\frac{15+36i}{117}$

$=\frac{3\left ( 5+12i \right )}{3\left ( 39 \right )}$

$=\frac{5+12i}{39}$

Report an Error

Example Question #8 : Complex Numbers

Which of the following represents 6-3i graphically?

Possible Answers:

Screen shot 2020 08 04 at 12.45.00 pm

Screen shot 2020 08 04 at 12.44.20 pm

Screen shot 2020 08 04 at 12.38.00 pm

Screen shot 2020 08 04 at 12.40.28 pm

Correct answer:

Screen shot 2020 08 04 at 12.38.00 pm

Explanation:

To represent complex numbers graphically, we treat the x-axis as the "axis of reals" and the y-axis as the "axis of imaginaries." To plot 6-3i , we want to move 6 units on the x-axis and -3 units on the y-axis. We can plot the point P to represent 6-3i , but we can also represent it by drawing a vector from the origin to point P. Both representations are in the diagram below.

Screen shot 2020 08 04 at 12.38.00 pm

Report an Error

Example Question #2 : Complex Numbers

The following graph represents which one of the following?

Screen shot 2020 08 04 at 1.04.02 pm

Possible Answers:

$\left (4+2i \right )+\left ( 1+3i \right )=\left ( 6+4i \right )$

$\left (4+2i \right )+\left ( 3+i \right )=\left ( 7+3i \right )$

$\left (4+i \right )+\left ( 2+3i \right )=\left ( 6+4i \right )$

$\left (4+3i \right )+\left ( 1+2i \right )=\left ( 5+5i \right )$

Correct answer:

$\left (4+i \right )+\left ( 2+3i \right )=\left ( 6+4i \right )$

Explanation:

We can take any complex number a+bi and graph it as a vector, measuring units in the x direction and units in the y direction. Therefore V_1=4+i . Likewise, V_2=2+3i . Then, we can add these two vectors together, summing their real parts and their imaginary parts to create their resultant vector R=6+4i . Therefore the correct answer is $\left (4+i \right )+\left ( 2+3i \right )=\left ( 6+4i \right )$ .

Report an Error

View Trigonometry Tutors

Ivory
Certified Tutor

Hopkinsville Community College, Associate, Associates in Science. Western Kentucky University, Bachelor in Arts, Psychology.

View Trigonometry Tutors

Ian
Certified Tutor

Lipscomb University, Bachelor of Science, Biology, General.

View Trigonometry Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Trigonometry Tutors in Top Cities:

Popular Courses & Classes

GRE Courses & Classes in Houston, SSAT Courses & Classes in Phoenix, Spanish Courses & Classes in San Diego, ACT Courses & Classes in Los Angeles, GRE Courses & Classes in Miami, SAT Courses & Classes in Atlanta, MCAT Courses & Classes in Denver, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Chicago, SAT Courses & Classes in Seattle

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Houston, GMAT Test Prep in Boston, SSAT Test Prep in Miami, LSAT Test Prep in Boston, LSAT Test Prep in Houston, MCAT Test Prep in New York City, GRE Test Prep in Miami, ISEE 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

Trigonometry : Complex Numbers

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Complex Numbers

Example Question #1 : Complex Numbers

Example Question #3 : Complex Numbers

Example Question #1 : Complex Numbers

Example Question #2 : Complex Numbers

Example Question #5 : Complex Numbers

Example Question #6 : Complex Numbers

Example Question #7 : Complex Numbers

Example Question #8 : Complex Numbers

Example Question #2 : Complex Numbers

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: