We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Squaring / Square Roots / Radicals

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 Next →

Example Question #4 : How To Multiply Complex Numbers

Complex numbers take the form a+bi , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Distribute: 2(4+7i)

Possible Answers:

8+7i

$\textup{None of these are correct}$

8+14i

6+7i

4+14i

Correct answer:

8+14i

Explanation:

This equation can be solved very similarly to a binomial like a+bx . Distribution takes place into both the real and nonreal terms inside the complex number, where applicable.

2(4+7i)

$(2\cdot4) + (2\cdot 7i)$

8 + 14i

Report an Error

Example Question #5 : How To Multiply Complex Numbers

Complex numbers take the form a+bi , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Distribute and solve: 5(3+i) + 2(6+2i)

Possible Answers:

27 +3i

9 + 3i

27 + 9i

9 + 9i

$\textup{None of these answers are correct}$

Correct answer:

27 + 9i

Explanation:

This problem can be solved very similarly to a binomial like a+bx .

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

$((5\cdot3)+ (5 \cdot i)) + ((2 \cdot 6) + (2\cdot 2i))$

(15 + 5i) + (12 + 4i)

(15 + 12) + (5i + 4i)

27 + 9i

Report an Error

Example Question #1 : How To Multiply Complex Numbers

Complex numbers take the form a+bi , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Which of the following is equivalent to i^3 ?

Possible Answers:

$i^{82}$

$i^{1000}$

$i^{30}$

$i^{23}$

Correct answer:

$i^{23}$

Explanation:

When dealing with complex numbers, remember that $i = \sqrt{-1}$ .

If we square , we thus get $i^2 = (\sqrt{-1})^2 = -1$ .

Yet another exponent gives us $i^3 = i^2 \cdot i = -1 \cdot i = -i$ OR $-\sqrt{-1}$ .

But when we hit i^4 , we discover that $i^4 = i^2 \cdot i^2 = -1 \cdot -1 = 1$

Thus, we have a repeating pattern with powers of , with every 4 exponents repeating the pattern. This means any power of evenly divisible by 4 will equal 1, any power of divisible by 4 with a remainder of 1 will equal , and so on.

Thus, $i^{23}$

$\frac{23}{4} = 5 \frac{3}{4}$

Since the remainder is 3, we know that $i^{23} = i^3 = -i$ .

Report an Error

Example Question #7 : How To Multiply Complex Numbers

Simplify the following:

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

Possible Answers:

Correct answer:

Explanation:

Begin by treating this just like any normal case of FOIL. Notice that this is really the form of a difference of squares. Therefore, the distribution is very simple. Thus:

(4-3i)(4+3i)=16-9i^2

Now, recall that $i=\sqrt{-1}$ . Therefore, i^2 is . Based on this, we can simplify further:

16-9(-1)=16+9=25

Report an Error

Example Question #8 : How To Multiply Complex Numbers

Which of the following is equal to -16i^6 ?

Possible Answers:

16i

Correct answer:

Explanation:

Remember that since $i = \sqrt{-1}{}$ , you know that i^2 is . Therefore, i^4 is -1*-1 or . This makes our question very easy.

i^6 is the same as i^4*i^2 or 1 * -1

Thus, we know that -16i^6 is the same as -16 * -1 or .

Report an Error

Example Question #9 : How To Multiply Complex Numbers

Complex numbers take the form a+bi , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Simplify the following expression, leaving no complex numbers in the denominator.

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

Possible Answers:

$\frac{8+ 3i}{32}$

$\frac{1+5i}{8}$

$\frac{20-4i}{15}$

$\frac {3+3i}{4}$

$\frac{-2+4i}{8}$

Correct answer:

$\frac{1+5i}{8}$

Explanation:

Solving this problem requires eliminating the nonreal term of the denominator. Our best bet for this is to cancel the nonreal term out by using the conjugate of the denominator.

Remember that for all binomials a+b , there exists a conjugate a-b such that $(a+b)\cdot(a-b) = (a^2-b^2)$ .

This can also be applied to complex conjugates, which will eliminate the nonreal portion entirely (since i^2 =-1 )!

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

$\frac{(3+2i)(4+4i)}{(4-4i)(4+4i)}$ Multiply both terms by the denominator's conjugate.

$\frac{(3+2i)(4+4i)}{(16-16i^2)} = \frac{(3+2i)(4+4i)}{32}$ Simplify. Note .

(3+2i)(4+4i) = (12 + 12i + 8i + 8i^2) FOIL the numerator.

Combine and simplify.

$\frac{4+20i}{32} = \frac{1+5i}{8}$ Simplify the fraction.

Thus, $\frac{3+2i}{4-4i} = \frac{1+5i}{8}$ .

Report an Error

← Previous 1 2 3 4 5 Next →

View ACT Math Tutors

Gary
Certified Tutor

SUNY at Albany, Bachelor of Science, Economics. Pace University-New York, Masters in Business Administration, Analysis and Fu...

View ACT Math Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View ACT Math Tutors

Joshua
Certified Tutor

Williams College, Bachelor in Arts, Chemistry.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

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

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in San Diego, MCAT Courses & Classes in Seattle, Spanish Courses & Classes in San Diego, GRE Courses & Classes in Chicago, SSAT Courses & Classes in San Diego, SAT Courses & Classes in Atlanta, MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Atlanta, LSAT Courses & Classes in Chicago

Popular Test Prep

GRE Test Prep in Chicago, LSAT Test Prep in Miami, GMAT Test Prep in Houston, GMAT Test Prep in Washington DC, SAT Test Prep in Houston, MCAT Test Prep in New York City, ACT Test Prep in Seattle, ACT Test Prep in Philadelphia, ISEE Test Prep in Phoenix, GRE Test Prep in Miami

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

ACT Math : Squaring / Square Roots / Radicals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : How To Multiply Complex Numbers

Example Question #5 : How To Multiply Complex Numbers

Example Question #1 : How To Multiply Complex Numbers

Example Question #7 : How To Multiply Complex Numbers

Example Question #8 : How To Multiply Complex Numbers

Example Question #9 : How To Multiply Complex Numbers

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: