We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Imaginary Numbers & Complex Functions

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Imaginary Roots Of Negative Numbers

$Simplify:\ \sqrt{-150}$

Possible Answers:

$5i\sqrt{3}$

$-5\sqrt{6}$

$-5\sqrt{3}$

$5i\sqrt{6}$

Correct answer:

$5i\sqrt{6}$

Explanation:

$When\ taking\ the\ square\ root\ of\ a\ negative\ number\ we\ must\ first\$

$i=\sqrt{-1}$

$\sqrt{-150}=\sqrt{-1}\sqrt{150}=i\sqrt{150}$

The perfect square of 25 will go into 150

$i\sqrt{150}=i\sqrt{25*6}$

The square root of 25 is 5.

$i\sqrt{25}\sqrt{6}=5i\sqrt{6}$

Report an Error

Example Question #12 : Imaginary Roots Of Negative Numbers

$Find\ all\ roots\ for: f(x)=3x^3-x^2+15x-5$

Possible Answers:

$\frac{1}{3},\ and\ i\sqrt{5}$

$\1,\and\ i\sqrt{5}$

$\1,\ i\sqrt{5}\ and\ -i\sqrt{5}$

$\frac{1}{3},\ i\sqrt{5}\ and\ -i\sqrt{5}$

Correct answer:

$\frac{1}{3},\ i\sqrt{5}\ and\ -i\sqrt{5}$

Explanation:

In order to find all the roots for the polynomial, we must use factor by grouping:

f(x)=3x^3-x^2+15x-5

We will group the 4 terms into two binomials:

(3x^3-x^2)+(15x-5)

We then take the greatest common factor out of each binomial:

x^2(3x-1)+5(3x-1)

We can see now that each term has a common binomial as a factor:

(3x-1)(x^2+5)

In order to find the roots, we must set each factor equal to zero and solve:

$3x-1=0\ which\ gives\ 3x=1\ then\ x=\frac{1}{3}$

$x^2+5=0\ which\ gives\ x^2=-5\ which\ results\ in\ x=\sqrt{-5}$

$This\ will\ give\ us\ imaginary\ roots\ of\ x=\pm i\sqrt{5}$

$The\ three\ roots\ are\ \frac{1}{3},\ i\sqrt{5}\ and\ -i\sqrt{5}$

Report an Error

Example Question #11 : Imaginary Numbers & Complex Functions

What are the imaginary root(s) of $\sqrt {-225}$ ?

Possible Answers:

-225i

-15i

15i

225i

Correct answer:

15i

Explanation:

Rewrite the expression as a positive root and the negative root

$\sqrt {-225}=\sqrt{225}\sqrt{-1}$

Take the square root of the positive root:

$\sqrt{225}\sqrt{-1}=15i$

To check the answer, square the square root:

(15i)^2=(15i)(15i)=(15^2)(i^2)=225(-1)=-225

should be what was inside the square root in the beginning.

It checks out, so the complex root is 15i

Report an Error

Example Question #12 : Imaginary Numbers & Complex Functions

$Simplify: \sqrt{-98}$

Possible Answers:

$-7\sqrt{2}$

$7\sqrt{2i}$

$7i\sqrt{2}$

$7\sqrt{-2}$

Correct answer:

$7i\sqrt{2}$

Explanation:

$Simplify: \sqrt{-98}$

$In\ order\ to\ simplify\ the\ square\ root\ of\ a\ negative\ number\\ we\ must\ first\ take\ the\ i\ out.$

$We\ can\ replace\ the\sqrt{-98}\ with\sqrt{(-1)(2)(49)}$

$\sqrt{-1}=i\\ \ \ \ \sqrt{2}=does\ not\ reduce\\ \sqrt{49}=7$

$Combining\ all\ of\ the\ above\ will\ give\ us\ 7i\sqrt{2}$

Report an Error

Example Question #1 : Operations On Complex Numbers

Expand and Simplify: (4-3i)(2+3i)(2-3i)

Possible Answers:

-20-15i

52-39i

39+52i

52+39i

Correct answer:

52-39i

Explanation:

Step 1: We will multiply the two complex conjugates: 2x-3 and 2x+3 .

(2-3i)(2+3i)=4+6i-6i-9i^2=4-9i^2

Step 2: Replace i^2 with .

4-9(-1)

Simplify:

4+9(1)
=13

Step 3: Multiply the result of the complex conjugates to the other parentheses, (4-3i) .

13(4-3i)=52-39i

The final answer after the product of all three binomials is 52-39i

Report an Error

Example Question #1 : Operations On Complex Numbers

Expand: $(i-1)^{10}$ .

Possible Answers:

-32i

32i

32(1-i)

Correct answer:

-32i

Explanation:

Quick Way:
Step 1: Expand (i-1)^2 .

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

Remember: i^2=-1

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

Step 2: $(1-i)^{10}=(i-1)^{2\cdot 5}$

By this equivalence, I can just raise the answer of (1-i)^2 to the power .

$(i-1)^{10}=(-2i)^{5}=-32i^5$

$i^5 \equiv i^1=i$ . Replace i^5 ..

Final answer: -32i

Long Way:

Math work

Report an Error

Example Question #261 : Gre Subject Test: Math

Multiply:

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

Possible Answers:

18-i

18+i

6+i

-i-18

Correct answer:

18+i

Explanation:

Step 1: FOIL:

Recall, FOIL means to multiply the first terms in both binomials together, the outer terms together, the inner terms together, and finally, the last terms together.

(2+3i)(3-4i)=6-8i+9i-12i^2

Step 2: Simplify:

6+i-12i^2

Step 3: Recall: i^2=-1 . Replace and simplify.

6+i-12(-1)
6+i+12
=18+i

Report an Error

Example Question #11 : Imaginary Numbers & Complex Functions

Simplify: (3-5i)+(2+7i)

Possible Answers:

5+2i

41+11i

6-35i

Correct answer:

5+2i

Explanation:

When adding imaginary numbers, simply add the real parts and the imaginary parts.

(3-5i)+(2+7i)= (3+2)+(-5i+7i)=5+2i

Report an Error

Example Question #1 : Operations On Complex Numbers

Simplify: (13-7i)-(10-8i)

Possible Answers:

3-15i

23-i

-74-174i

3+i

Correct answer:

3+i

Explanation:

$When\ subtracting\ binomials\ in\ ( )\; first\ distribute\ the\ negative\ sign.$

(13-7i)-(10-8i)=13-7i-10+8i

$Now\ combine\ like\ terms.$

13-10-7i+8i=3+i

Report an Error

Example Question #4 : Operations On Complex Numbers

What is the value of (3-4i)(2i+3) ?

Possible Answers:

None of the other answers

-6i+17

-6i+1

-6i-17

6i-17

Correct answer:

-6i+17

Explanation:

Distribute and Multiply:

(3-4i)(2i+3)=6i+9-8i^2-12i

Simplify all terms...

6i+9-8(-1)-12i

=6i+9+8-12i

=-6i+17

Report an Error

View Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View Tutors

Gregory
Certified Tutor

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

View Tutors

Abdul Azeez
Certified Tutor

University of Manitoba, Master's/Graduate, Business.

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Chicago, Physics Tutors in Boston, Biology Tutors in Miami, SSAT Tutors in Dallas Fort Worth, ISEE Tutors in Washington DC, MCAT Tutors in Washington DC, Calculus Tutors in Los Angeles, ISEE Tutors in New York City, MCAT Tutors in Seattle, LSAT Tutors in Dallas Fort Worth

Popular Courses & Classes

ACT Courses & Classes in Boston, Spanish Courses & Classes in Boston, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles, ACT Courses & Classes in Seattle, MCAT Courses & Classes in Boston, MCAT Courses & Classes in Atlanta, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Chicago, MCAT Courses & Classes in Houston

Popular Test Prep

ACT Test Prep in San Diego, SSAT Test Prep in Chicago, GMAT Test Prep in Los Angeles, ISEE Test Prep in Phoenix, LSAT Test Prep in Miami, SAT Test Prep in Miami, ACT Test Prep in Boston, ISEE Test Prep in Denver, SSAT Test Prep in San Diego, SAT Test Prep in Seattle

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

GRE Subject Test: Math : Imaginary Numbers & Complex Functions

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #11 : Imaginary Roots Of Negative Numbers

Example Question #12 : Imaginary Roots Of Negative Numbers

Example Question #11 : Imaginary Numbers & Complex Functions

Example Question #12 : Imaginary Numbers & Complex Functions

Example Question #1 : Operations On Complex Numbers

Example Question #1 : Operations On Complex Numbers

Example Question #261 : Gre Subject Test: Math

Example Question #11 : Imaginary Numbers & Complex Functions

Example Question #1 : Operations On Complex Numbers

Example Question #4 : Operations On Complex Numbers

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: