Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to multiply complex numbers

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Multiply Complex Numbers

Which of the following is equal to $\left (3i \right )^{5}$ ?

Possible Answers:

243i

None of the other responses is correct.

15i

-15i

-243i

Correct answer:

243i

Explanation:

By the power of a product property,

$\left (3i \right )^{5} = 3^{5} \cdot i^{5} = 3^{5} \cdot i^{4} \cdot i = 243 \cdot 1 \cdot i = 243 i$

Report an Error

Example Question #2 : How To Multiply Complex Numbers

Multiply:

(10 + 3i)(10-3i)

Possible Answers:

100 - 9i

100 + 9i

None of the other responses is correct.

109

Correct answer:

109

Explanation:

This is the product of a complex number and its complex conjugate. They can be multiplied using the pattern

$\left (A + Bi \right )\left (A - Bi \right ) = A^{2} + B^{2}$

with A = 10, B = 3

$(10 + 3i)(10-3i) = 10^{2} +3^{2} = 100 + 9 = 109$

Report an Error

Example Question #1 : How To Multiply Complex Numbers

Which of the following is equal to $i ^{-56}$ ?

Possible Answers:

Correct answer:

Explanation:

$i ^{-56} = \frac{1}{i^{56}}$

$56 \div 4 = 14$ , so 56 is a multiple of 4. raised to the power of any multiple of 4 is equal to 1, so

$i ^{-56} = \frac{1}{i^{56}} = \frac{1}{1} = 1$ .

Report an Error

Example Question #4 : How To Multiply Complex Numbers

Which of the following is equal to (2i)^7 ?

Possible Answers:

-128i

-2i

128i

Correct answer:

-128i

Explanation:

The first step to solving this problem is distributing the exponent:

2^7i^7 = 128i^7

Next, we need simplify the complex portion.

$i^7=i^2\times i^2\times i^2\times i=-1\times -1\times -1\times i=-i$

Thus, our final answer is $128\times (-i)=-128i$ .

Report an Error

Example Question #2 : How To Multiply Complex Numbers

What is the eighth power of ?

Possible Answers:

6,561i

None of the other responses is correct.

-24i

-6,561i

24i

Correct answer:

None of the other responses is correct.

Explanation:

$\left (3i \right )^{8}$

$= 3^{8} i^{8}$

$= 6,561 i^{8}$

raised to the power of any multiple of 4 is equal to 1, so the above expresion is equal to

$= 6,561 \cdot 1 = 6,561$

This is not among the given choices.

Report an Error

Example Question #4 : How To Multiply Complex Numbers

What is the third power of $2 + i\sqrt{5}$ ?

Possible Answers:

$38 +7i\sqrt{5}$

$-22 +17i\sqrt{5}$

$-22 +7i\sqrt{5}$

38 +35i

-22 +35i

Correct answer:

$-22 +7i\sqrt{5}$

Explanation:

You are being asked to evaluate

$\left (2 + i\sqrt{5} \right )^{3}$

You can use the cube of a binomial pattern with $A = 2, B = i\sqrt{5}$ :

$\left ( A + B \right )^{3} = A^{3}+ 3A^{2}B + 3AB^{2}+ B^{3}$

$\left ( 2 + i\sqrt{5} \right )^{3} =2^{3}+ 3 \cdot 2^{2} \cdot i\sqrt{5} + 3 \cdot 2 (i\sqrt{5}) ^{2}+ (i\sqrt{5}) ^{3}$

$=8+ 3 \cdot 4 \cdot i\sqrt{5} + 6i ^{2} (\sqrt{5}) ^{2}+ i^{3}(\sqrt{5}) ^{3}$

$=8+12i\sqrt{5} + 6 (-1) 5+(-i)(5\sqrt{5})$

$=8-30 +12i\sqrt{5} -5i\sqrt{5}$

$=-22 +7i\sqrt{5}$

Report an Error

Example Question #5 : How To Multiply Complex Numbers

What is the fourth power of $3 - i\sqrt{2}$ ?

Possible Answers:

$121-84 i\sqrt{2}}$

$-23-84 i\sqrt{2}}$

$49- 132 i\sqrt{2}$

-23-168i

95-168i

Correct answer:

$-23-84 i\sqrt{2}}$

Explanation:

$\left (3 - i\sqrt{2} \right )^{4}$ can be calculated by squaring $3 - i\sqrt{2}$ , then squaring the result, using the square of a binomial pattern as follows:

$\left (3 - i\sqrt{2} \right )^{2}$

$=3^{2}- 2 \cdot 3 \cdot i\sqrt{2} +\left ( i\sqrt{2} \right )^{2}$

$=9- 6 i\sqrt{2} +2i^{2}$

$=9- 6 i\sqrt{2} +2(-1)$

$=7- 6 i\sqrt{2}$

$\left (3 - i\sqrt{2} \right )^{4}$

$=\left [ \left (3 - i\sqrt{2} \right )^{2} \right ]^{2}$

$=\left (7- 6 i\sqrt{2}} \right )^{2}$

$=7^{2} - 2 \cdot 7 \cdot 6 i\sqrt{2}} + \left ( 6 i\sqrt{2}} \right )^{2}$

$=49-84 i\sqrt{2}} + 6^{2} i^{2} \left ( \sqrt{2}} \right )^{2}$

$=49-84 i\sqrt{2}} +36 (-1) (2)$

$=49-84 i\sqrt{2}} -72$

$=-23-84 i\sqrt{2}}$

Report an Error

Example Question #13 : Complex Numbers

Multiply 32+ 18i by its complex conjugate. What is the product?

Possible Answers:

1,152

700 + 1,152i

700

700 - 1,152i

1,348

Correct answer:

1,348

Explanation:

The product of any complex number a + bi and its complex conjugate a - bi is the real number $a^{2}+b^{2}$ , so all that is needed here is to evaluate the expression:

$32^{2}+ 18 ^{2}= 1,024+ 324 = 1,348$

Report an Error

Example Question #6 : How To Multiply Complex Numbers

What is the eighth power of 1+ i ?

Possible Answers:

The correct response is not given among the other choices.

256i

8 - 8i

8 + 8i

Correct answer:

Explanation:

First, square 1+ i using the square of a binomial pattern as follows:

$\left (1+ i \right )^{2}$

$= 1^{2}+ 2 \cdot 1 \cdot i + i^{2}$

= 1 +2i -1

= 2i

Raising this number to the fourth power yields the correct response:

$\left (1+ i \right )^{8}$

$= \left [\left (1+ i \right )^{2} \right ]^{4}$

$= (2i)^{4}$

$= (2 )^{4} \cdot i^{4}$

$=16 \cdot 1 = 16$

Report an Error

Example Question #7 : How To Multiply Complex Numbers

What is the ninth power of -2i ?

Possible Answers:

-512 i

None of the other responses is correct.

18i

-18i

512 i

Correct answer:

-512 i

Explanation:

$\left ( -2i\right )^{9}$

$= \left ( -2 \right )^{9} \cdot i^{9}$

To raise a negative number to an odd power, take the absolute value of the base to that power and give its opposite:

$\left ( -2\right )^{9} = - \left ( 2^{9}\right ) = -512$

To raise to a power, divide the power by 4 and raise to the remainder. Since

$9 \div 4 = 2 \textup{ R }1$ ,

$i^{9} = i^{1}= i$

Therefore,

$\left ( -2i\right )^{9}= \left ( -2 \right )^{9} \cdot i^{9} = -512 i$

Report an Error

View PSAT Mathematics Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View PSAT Mathematics Tutors

Paul
Certified Tutor

University of Phoenix-Albuquerque Campus, Bachelor of Science, Computer and Information Systems Security.

View PSAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Miami, MCAT Tutors in Atlanta, SSAT Tutors in Los Angeles, SSAT Tutors in Denver, Reading Tutors in Chicago, GRE Tutors in Houston, Spanish Tutors in Houston, Chemistry Tutors in New York City, Statistics Tutors in Dallas Fort Worth, English Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Washington DC, LSAT Courses & Classes in Denver, GMAT Courses & Classes in San Diego, SAT Courses & Classes in Los Angeles, ACT Courses & Classes in Boston, MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Denver, GMAT Courses & Classes in Chicago, ISEE Courses & Classes in Houston, ACT Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in Atlanta, GMAT Test Prep in Chicago, ACT Test Prep in Houston, LSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Seattle, ISEE Test Prep in Philadelphia, GMAT Test Prep in Los Angeles, ISEE Test Prep in San Diego, SAT Test Prep in Los Angeles, ISEE 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

PSAT Math : How to multiply complex numbers

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Multiply Complex Numbers

Example Question #2 : How To Multiply Complex Numbers

Example Question #1 : How To Multiply Complex Numbers

Example Question #4 : How To Multiply Complex Numbers

Example Question #2 : How To Multiply Complex Numbers

Example Question #4 : How To Multiply Complex Numbers

Example Question #5 : How To Multiply Complex Numbers

Example Question #13 : Complex Numbers

Example Question #6 : How To Multiply Complex Numbers

Example Question #7 : How To Multiply Complex Numbers

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: