We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Exponents

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

Example Question #2 : Complex Numbers

What is the solution of the following equation?

$3\left ( 8 + 5i\right ) + \frac{1}{2}\left (4 + 2i\right ) = ?$

Possible Answers:

39 + 3i

13 + 6i

24 +i

26 + 16i

12 + 7i

Correct answer:

26 + 16i

Explanation:

A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.

First, distribute:

$3\left ( 8 + 5i\right ) + \frac{1}{2}\left (4 + 2i\right )$

$\left ( 24 + 15i\right ) + \left (2 + i\right )$

Then, group the real and imaginary components:

$\left ( 24 + 2\right ) + i\left (15 + 1\right )$

Solve to get:

26 + 16i

Report an Error

Example Question #835 : Algebra

What is the sum of and given

a = 5 + 3i

and

b = 2 + i ?

Possible Answers:

3 + 2i

7 + 4i

5 + 6i

Correct answer:

7 + 4i

Explanation:

A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.

In equation , is the real component and is the imaginary component (designated by ).

In equation , is the real component and is the imaginary component.

When added,

$a + b = \left ( 5+3i\right ) + \left ( 2 + i\right ) = \left ( 5 + 2\right ) + i\left ( 3 + 1\right ) = 7 + 4i$

Report an Error

Example Question #5 : Complex Numbers

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

Simplify: (5 +7i) + (17-4i)

Possible Answers:

22 +11i

-12 +3i

-12-3i

22-3i

22+3i

Correct answer:

22+3i

Explanation:

When adding or subtracting complex numbers, the real terms are additive/subtractive, and so are the nonreal terms.

(5 +7i) + (17-4i) = (5+17) + (7i - 4i) = 22 + 3i

Report an Error

Example Question #6 : Complex Numbers

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

Can you add the following two numbers: $3+7i \textup{ and } 8$ ? If so, what is their sum?

Possible Answers:

$\textup{Yes, } 3 + 7i + 8$

$\textup{Yes, } 11 + 15i$

$\textup{Yes, }3 + 15i$

$\textup{Yes, } 11+ 7i$

$\textup{No, the two numbers cannot be added because one is complex and one is not.}$

Correct answer:

$\textup{Yes, } 11+ 7i$

Explanation:

Complex numbers take the form a + bi, where a is the real term in the complex number and bi is the nonreal (imaginary) term in the complex number. Taking this, we can see that for the real number 8, we can rewrite the number as 8 + 0i , where represents the (zero-sum) non-real portion of the complex number.

Thus, any real number can be added to any complex number simply by considering the nonreal portion of the number to be .

Report an Error

Example Question #1 : How To Add 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 incorrect?

Possible Answers:

(2-i) + (-2+i) = 0

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

(3+7i) - (2+2i) = 1 +9i

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

(3+3i) - (3-3i) = 0+ 6i

Correct answer:

(3+7i) - (2+2i) = 1 +9i

Explanation:

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.

Thus, to balance the equation, add like terms on the left side.

(3+7i) - (2+2i) = 1 +9i

(3-2) + (7i-2i) = 1+9i

$1+5i \neq 1+9i$

Report an Error

Example Question #1 : How To Divide Complex Numbers

Simplify: $\frac{9+4i}{4i}$

Possible Answers:

$-\frac{ 9 }{4 } + i$

$\frac{ 9 }{4 } - i$

$1+ \frac{ 9 }{4 } i$

$\frac{ 9 }{4 } + i$

$1- \frac{ 9 }{4 } i$

Correct answer:

$1- \frac{ 9 }{4 } i$

Explanation:

Multiply both numberator and denominator by :

$\frac{9+4i}{4i}$

$= \frac{\left (9+4i \right )\cdot i}{4i \cdot i}$

$= \frac{9i + 4i^{2}}{4 i^{2}}$

$= \frac{9i + 4 (-1)}{4 (-1)}$

$= \frac{-4+9i }{-4 }$

$= \frac{-4 }{-4 }+ \frac{ 9i }{-4 }$

$= 1- \frac{ 9 }{4 } i$

Report an Error

Example Question #1 : How To Divide Complex Numbers

Evaluate: $100 \div 5i \div 5i$

Possible Answers:

100i

-4i

Correct answer:

Explanation:

First, divide 100 by as follows:

$\frac{100}{5i} = \frac{100 \cdot i}{5i \cdot i} = \frac{100 i}{5(-1)} = \frac{100 i}{-5}= -20i$

Now dvide this result by :

$\frac{-20i}{5i} = \frac{-20}{5} = -4$

Report an Error

Example Question #3 : How To Divide Complex Numbers

Evaluate: $100 \div (1+i) \div (1-i)$

Possible Answers:

-25 +25i

25+ 25i

25-25i

Correct answer:

Explanation:

First, divide 100 by 1+i as follows:

$\frac{100}{1+i}$

$=\frac{100(1-i)}{\left (1+i \right )(1-i)}$

$= \frac{100-100i}{1^{2}+1^{2}}$

$= \frac{100-100i}{2}$

= 50-50i

Now, divide this by 1-i :

$\frac{ 50-50i}{1-i} = \frac{ 50 (1-i)}{1-i} = 50$

Report an Error

Example Question #1 : How To Divide Complex Numbers

Evaluate: $100i \div (4i )^{2}$

Possible Answers:

$-\frac{25}{2}$

$\frac{25}{4}i$

$- \frac{25}{4}i$

$\frac{25}{2}i$

$- \frac{25}{4}$

Correct answer:

$- \frac{25}{4}i$

Explanation:

First, evaluate $(4i)^{2}$ :

$\left (4i \right )^{2} = 16 i^{2} = 16 (-1)= -16$

Now divide this into 100 i :

$\frac{100 i}{-16} =- \frac{25}{4}i$

Report an Error

Example Question #5 : How To Divide Complex Numbers

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

Possible Answers:

$\frac{1}{2} i$

$\frac{1}{2}$

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

Correct answer:

$\frac{1}{2}$

Explanation:

First, evaluate $\left ( 1+ i\right )^{2}$ using the square pattern:

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

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

=1+2i+ (-1)

=2i

Divide this into :

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

Report an Error

View ACT Math Tutors

MEER
Certified Tutor

IIT , Master's/Graduate, Microelectronics .

View ACT Math Tutors

Margaret
Certified Tutor

View ACT Math Tutors

Sarah
Certified Tutor

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

GRE Courses & Classes in Denver, Spanish Courses & Classes in Houston, GMAT Courses & Classes in New York City, GMAT Courses & Classes in Washington DC, ISEE Courses & Classes in Atlanta, Spanish Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix, GRE Courses & Classes in Washington DC

Popular Test Prep

SAT Test Prep in New York City, GRE Test Prep in Phoenix, LSAT Test Prep in New York City, SSAT Test Prep in Los Angeles, MCAT Test Prep in Atlanta, SAT Test Prep in Denver, GMAT Test Prep in Atlanta, GMAT Test Prep in New York City, GMAT Test Prep in Washington DC, SSAT Test Prep in Atlanta

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 : Exponents

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2 : Complex Numbers

Example Question #835 : Algebra

Example Question #5 : Complex Numbers

Example Question #6 : Complex Numbers

Example Question #1 : How To Add Complex Numbers

Example Question #1 : How To Divide Complex Numbers

Example Question #1 : How To Divide Complex Numbers

Example Question #3 : How To Divide Complex Numbers

Example Question #1 : How To Divide Complex Numbers

Example Question #5 : How To Divide Complex Numbers

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: