Adding and Subtracting Complex Numbers

Adding and Subtracting Complex Numbers

Learn more about the complex numbers and how to add and subtract them using the following step-by-step guide.

Step by step guide to add and subtract the Complex Numbers

  • A complex number is expressed in the form \(a+bi\), where \(a\) and \(b\) are real numbers, and \(i\), which is called an imaginary number, is \(a \) solution of the equation \(x^2=-1\)
  • For adding complex numbers: \((a+bi)+(c+di)=(a+c)+(b+d)i\)
  • For subtracting complex numbers: \((a+bi)-(c+di)=(a-c)+(b-d)i\)

Example 1:

Solve: \(10+(-5-3i)-2\)

Solution:

Remove parentheses: \(10+(-5-3i)-2→10-5-3i-2\)
Combine like terms: \(10-5-3i-2=3-3i\)

Example 2:

Solve: \(-3+(4i)+(9-2i)\)

Solution:

Remove parentheses: \(-3+(4i)+(9-2i)→-3+4i+9-2i\)
Group like terms: \(-3+4i+9-2i→6+2i\)

Example 3:

Solve: \((-8+2i)+(-8+6i)\)

Solution:

Remove parentheses: \((-8+2i)+(-8+6i)=-8+2i-8+6i\)
Group like terms: \(-8+2i-8+6i→-8-8+2i+6i\)
Add similar terms: \(-8-8+2i+6i=-16+8i\)

Example 4:

Solve: \((6-3i)-(-8-7i)\)

Solution:

Remove parentheses by multiplying the negative sign to the second parenthesis: \((6-3i)-(-8-7i)=6-3i+8+7i\)
Combine like terms: \(6-3i+8+7i=14+4i\)

Exercises

Simplify.

  • \(\color{blue}{– 8 + (2i) + (– 8 + 6i)}\)
  • \(\color{blue}{12 – (5i) + (4 – 14i)}\)
  • \(\color{blue}{– 2 + (– 8 – 7i) – 9}\)
  • \(\color{blue}{(– 18 – 3i) + (11 + 5i)}\)
  • \(\color{blue}{(3 + 5i) – (8 + 3i)}\)
  • \(\color{blue}{(8 – 3i) – (4 + i)}\)

Download Adding and Subtracting Complex Numbers Worksheet

  • \(\color{blue}{– 16 + 8i}\)
  • \(\color{blue}{16 – 19i}\)
  • \(\color{blue}{–19 – 7i}\)
  • \(\color{blue}{–7 + 2i}\)
  • \(\color{blue}{-5 + 2i}\)
  • \(\color{blue}{4 – 4i}\)

Related to "Adding and Subtracting Complex Numbers"

Grade 3 MCAS Math Worksheets
Grade 3 MCAS Math Worksheets
FREE Grade 6 OST Math Practice Test
FREE Grade 6 OST Math Practice Test
MAP Math Grade 8 Practice Test Questions
MAP Math Grade 8 Practice Test Questions
Top 10 Grade 4 MAP Math Practice Questions
Top 10 Grade 4 MAP Math Practice Questions
Full-Length ASVAB Math Practice Test-Answers and Explanations
Full-Length ASVAB Math Practice Test-Answers and Explanations
Full-Length ASVAB Math Practice Test
Full-Length ASVAB Math Practice Test
SBAC Grade 4 Math FREE Sample Practice Questions
SBAC Grade 4 Math FREE Sample Practice Questions
Grade 3 PSSA Math Worksheets
Grade 3 PSSA Math Worksheets
FREE Grade 8 NYSE Math Practice Test
FREE Grade 8 NYSE Math Practice Test
NYSE Math Grade 8 Practice Test Questions
NYSE Math Grade 8 Practice Test Questions

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…