Just as with real numbers, we can perform arithmetic operations on complex numbers. To add or subtract complex numbers, we combine the real parts and combine the imaginary parts.
A General Note: Addition and Subtraction of Complex Numbers
Adding complex numbers:
[latex]\left(a+bi\right)+\left(c+di\right)=\left(a+c\right)+\left(b+d\right)i[/latex]
Subtracting complex numbers:
[latex]\left(a+bi\right)-\left(c+di\right)=\left(a-c\right)+\left(b-d\right)i[/latex]
How To: Given two complex numbers, find the sum or difference.
- Identify the real and imaginary parts of each number.
- Add or subtract the real parts.
- Add or subtract the imaginary parts.
Example 3: Adding Complex Numbers
Add [latex]3 - 4i[/latex] and [latex]2+5i[/latex].
Solution
We add the real parts and add the imaginary parts.
[latex]\begin{cases}\left(a+bi\right)+\left(c+di\right)=\left(a+c\right)+\left(b+d\right)i\hfill \\ \left(3 - 4i\right)+\left(2+5i\right)=\left(3+2\right)+\left(-4+5\right)i\hfill \\ \text{ }=5+i\hfill \end{cases}[/latex]
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- College Algebra. Authored by: OpenStax College Algebra. Provided by: OpenStax. Located at: http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface. License: CC BY: Attribution
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- Ex 1: Adding and Subtracting Complex Numbers. Authored by: Mathispower4u. Located at: https://youtu.be/SGhTjioGqqA. License: All Rights Reserved. License Terms: Standard YouTube License