Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to add complex numbers

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : Complex Numbers

Simplify: $\sqrt{-3}+\sqrt{-9}+\sqrt{-16}$

Possible Answers:

$i\sqrt3 -7i$

$i\sqrt3 +i$

$i\sqrt3 +7i$

$2i\sqrt7$

$i\sqrt3-i$

Correct answer:

$i\sqrt3 +7i$

Explanation:

Rewrite $\sqrt{-3}+\sqrt{-9}+\sqrt{-16}$ in their imaginary terms.

$i=\sqrt{-1}$

$\sqrt{-3}+\sqrt{-9}+\sqrt{-16}=i\sqrt3+3i+4i = i\sqrt3 +7i$

Report an Error

Example Question #1 : Complex Numbers

Add $5 + i \sqrt {5 }$ and its complex conjugate.

Possible Answers:

$-2 i \sqrt{5}$

$2 i \sqrt{5}$

Correct answer:

Explanation:

The complex conjugate of a complex number a+ bi is a - bi . Therefore, the complex conjugate of $5 + i \sqrt {5 }$ is $5 - i \sqrt {5 }$ ; add them by adding real parts and adding imaginary parts, as follows:

$(5 + i \sqrt {5 } )+( 5 - i \sqrt {5 })$

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

= 10 ,

the correct response.

Report an Error

Example Question #3 : Complex Numbers

Add $13 - i \sqrt{13}$ to its complex conjugate.

Possible Answers:

$2i \sqrt{13}$

$-2i \sqrt{13}$

Correct answer:

Explanation:

The complex conjugate of a complex number a - bi is a+ bi . Therefore, the complex conjugate of $13 - i \sqrt{13}$ is $13 + i \sqrt{13}$ ; add them by adding real parts and adding imaginary parts, as follows:

$(13 - i \sqrt{13} )+( 13 + i \sqrt{13})$

$= 13+13 - i \sqrt {13 }+ i \sqrt {13}$

= 26

Report an Error

Example Question #2 : Complex Numbers

An arithmetic sequence begins as follows:

3, 3i, ...

Give the next term of the sequence

Possible Answers:

3+ 6i

3- 6i

-3 + 6i

Correct answer:

-3 + 6i

Explanation:

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

d = 3i - 3 = -3 + 3i

Add this to the second term to obtain the desired third term:

$a_{3} = a_{2} +d = 3i + ( -3 + 3i) = -3 + 3i + 3i = -3 + 6i$ .

Report an Error

Example Question #3 : Complex Numbers

Simplify: (3+5i)+(4-2i)+(-2+i)

Possible Answers:

5-4i

10-9i

9-8i

9+8i

5+4i

Correct answer:

5+4i

Explanation:

It can be easier to line real and imaginary parts vertically to keep things organized, but in essence, combine like terms (where 'like' here means real or imaginary):

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

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

=5+4i

Report an Error

Example Question #2 : Complex Numbers

For $i=\sqrt{-1}$ , what is the sum of $\frac{3}{2} + \frac{1}{4} i$ and its complex conjugate?

Possible Answers:

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

$\frac{1}{2} i$

$\frac{7}{4} + \frac{7}{4} i$

Correct answer:

Explanation:

The complex conjugate of a complex number a+bi is a - bi , so $\frac{3}{2} + \frac{1}{4} i$ has $\frac{3}{2} - \frac{1}{4} i$ as its complex conjugate. The sum of the two numbers is

$\left (\frac{3}{2} + \frac{1}{4} i \right ) + \left ( \frac{3}{2} - \frac{1}{4} i \right )$

$= \frac{3}{2} + \frac{1}{4} i + \frac{3}{2} - \frac{1}{4} i$

$= \frac{3}{2} + \frac{3}{2} + \frac{1}{4} i - \frac{1}{4} i$

Report an Error

Example Question #3 : How To Add Complex Numbers

Evaluate:

$9i^{9}+ 10 i^{10}+ 11 i^{11}+ 12 i^{12}$

Possible Answers:

2 +2i

-2 - 2i

None of these

2 - 2i

-2+ 2i

Correct answer:

2 - 2i

Explanation:

A power of can be evaluated by dividing the exponent by 4 and noting the remainder. The power is determined according to the following table:

$\begin{matrix} \textrm{\underline{Rem}}& \textrm{\underline{Power}} \\ 0& 1\\ 1& i\\ 2& -1\\ 3& -i \end{matrix}$

$9 \div 4 = 2 \textrm{ R }1$ , so $i^{9} = i$

$10 \div 4 = 2 \textrm{ R }2$ , so $i^{10} = -1$

$11 \div 4 = 2 \textrm{ R }3$ , so $i^{11} = - i$

$12 \div 4 = 3 \textrm{ R }0$ , so $i^{12} = 1$

Substituting:

$9i^{9}+ 10 i^{10}+ 11 i^{11}+ 12 i^{12}$

= 9(i) + 10 (-1)+ 11 (-i)+ 12 (1)

= 9i - 10 - 11i+ 12

Collect real and imaginary terms:

- 10 + 12 + 9i - 11i

= 2 - 2i

Report an Error

Example Question #3 : How To Add Complex Numbers

Evaluate:

$i^{6} + i^{7}+ i^{8}+ i^{9}$

Possible Answers:

-2i

Correct answer:

Explanation:

A power of can be evaluated by dividing the exponent by 4 and noting the remainder. The power is determined according to the following table:

$\begin{matrix} \textrm{\underline{Rem}}& \textrm{\underline{Power}} \\ 0& 1\\ 1& i\\ 2& -1\\ 3& -i \end{matrix}$

$6 \div 4 = 1 \textrm{ R }2$ , so $i^{6} = -1$

$7 \div 4 = 1 \textrm{ R }3$ , so $i^{7} = -i$

$8 \div 4 = 2 \textrm{ R }0$ , so $i^{8} = 1$

$9 \div 4 = 2 \textrm{ R }1$ , so $i^{9} = i$

Substituting:

$i^{6} + i^{7}+ i^{8}+ i^{9}$

= -1+ ( - i )+ 1 +i

= -1 + 1 - i + i

= 0

Report an Error

View SAT Mathematics Tutors

Miriam
Certified Tutor

Washington University in St Louis, Bachelor in Arts, Biology, General.

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Irina
Certified Tutor

New York University, Bachelors, Biochemistry.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

LSAT Courses & Classes in Chicago, GRE Courses & Classes in Boston, Spanish Courses & Classes in Denver, LSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Atlanta, SSAT Courses & Classes in Chicago, MCAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in Seattle, LSAT Test Prep in Chicago, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Atlanta, GRE Test Prep in Atlanta, SAT Test Prep in New York City, ISEE Test Prep in Denver, LSAT Test Prep in Boston, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Los Angeles

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

SAT Math : How to add complex numbers

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #4 : Complex Numbers

Example Question #1 : Complex Numbers

Example Question #3 : Complex Numbers

Example Question #2 : Complex Numbers

Example Question #3 : Complex Numbers

Example Question #2 : Complex Numbers

Example Question #3 : How To Add Complex Numbers

Example Question #3 : How To Add Complex Numbers

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: