How to Add and Subtract Complex Numbers

How to Add and Subtract Complex Numbers

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

Related Topics

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: \((a+bi)-(c+di)=(a-c)+(b-d)i\)

Adding and Subtracting Complex Numbers – Example 1:

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

Solution:

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

Adding and Subtracting Complex Numbers – Example 2:

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

Solution:

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

Adding and Subtracting Complex Numbers – 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: \(-8-8+2i+6i=-16+8i\)

Adding and Subtracting Complex Numbers – 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 for Adding and Subtracting Complex Numbers

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 "How to Add and Subtract Complex Numbers"

Top 10 Tips to Create a TABE Math Study Plan
Top 10 Tips to Create a TABE Math Study Plan
10 Most Common PSAT 10 Math Questions
10 Most Common PSAT 10 Math Questions
Top 10 Tips to Overcome HiSET Math Anxiety
Top 10 Tips to Overcome HiSET Math Anxiety
Top 10 Tips to Create a HiSET Math Study Plan
Top 10 Tips to Create a HiSET Math Study Plan
Top 10 PSAT 10 Math Practice Questions
Top 10 PSAT 10 Math Practice Questions
PSAT 10 Math Formulas
PSAT 10 Math Formulas
The Ultimate PSAT 10 Math Formula Cheat Sheet
The Ultimate PSAT 10 Math Formula Cheat Sheet
Top 10 Tips You MUST Know to Retake the PSAT/NMSQT Math
Top 10 Tips You MUST Know to Retake the PSAT/NMSQT Math
The Ultimate PSAT 10 Math Course
The Ultimate PSAT 10 Math Course
PSAT 10 Math Worksheets
PSAT 10 Math Worksheets

Leave a Reply

Your email address will not be published.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

36% OFF

Download Instantly

X

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…