Adding and Subtracting Complex Numbers: A Comprehensive Guide
Complex numbers are an essential concept in mathematics, and being able to add and subtract them is a crucial skill. In this guide, we will take you through the basics of adding and subtracting complex numbers, including examples and a worksheet to practice.
What are Complex Numbers?
Complex numbers are numbers that can be expressed in the form a + bi, where:
- a is the real part of the number
- b is the imaginary part of the number
- i is the imaginary unit, which is defined as the square root of -1
Adding Complex Numbers
To add complex numbers, we simply add the real parts and the imaginary parts separately. The formula for adding complex numbers is:
(a + bi) + (c + di) = (a + c) + (b + d)i
Here’s an example:
Example 1: Add 3 + 4i and 2 + 5i
Solution:
(3 + 4i) + (2 + 5i) = (3 + 2) + (4 + 5)i = 5 + 9i
Subtracting Complex Numbers
To subtract complex numbers, we subtract the real parts and the imaginary parts separately. The formula for subtracting complex numbers is:
(a + bi) - (c + di) = (a - c) + (b - d)i
Here’s an example:
Example 2: Subtract 3 + 4i from 2 + 5i
Solution:
(2 + 5i) - (3 + 4i) = (2 - 3) + (5 - 4)i = -1 + i
Multiplying and Dividing Complex Numbers
While we’re not focusing on multiplying and dividing complex numbers in this guide, it’s worth noting that these operations are also possible.
Worksheet
Now that you’ve learned how to add and subtract complex numbers, it’s time to practice! Here’s a worksheet with 10 questions to get you started:
| Question | Complex Numbers | Answer |
|---|---|---|
| 1 | (2 + 3i) + (4 + 2i) | |
| 2 | (5 + 2i) - (3 + 4i) | |
| 3 | (1 + 2i) + (2 + 3i) | |
| 4 | (4 + 5i) - (2 + 3i) | |
| 5 | (3 + 4i) + (1 + 2i) | |
| 6 | (2 + 5i) - (4 + 3i) | |
| 7 | (5 + 3i) + (2 + 1i) | |
| 8 | (1 + 3i) - (2 + 4i) | |
| 9 | (4 + 2i) + (3 + 5i) | |
| 10 | (2 + 1i) - (5 + 2i) |
Solutions
Here are the solutions to the worksheet:
| Question | Complex Numbers | Answer |
|---|---|---|
| 1 | (2 + 3i) + (4 + 2i) | 6 + 5i |
| 2 | (5 + 2i) - (3 + 4i) | 2 - 2i |
| 3 | (1 + 2i) + (2 + 3i) | 3 + 5i |
| 4 | (4 + 5i) - (2 + 3i) | 2 + 2i |
| 5 | (3 + 4i) + (1 + 2i) | 4 + 6i |
| 6 | (2 + 5i) - (4 + 3i) | -2 + 2i |
| 7 | (5 + 3i) + (2 + 1i) | 7 + 4i |
| 8 | (1 + 3i) - (2 + 4i) | -1 - i |
| 9 | (4 + 2i) + (3 + 5i) | 7 + 7i |
| 10 | (2 + 1i) - (5 + 2i) | -3 - i |
📝 Note: Make sure to check your answers carefully and review the examples if you need help.
In conclusion, adding and subtracting complex numbers is a straightforward process that involves adding or subtracting the real and imaginary parts separately. With practice, you’ll become more comfortable working with complex numbers and be able to tackle more advanced math concepts.
What is the formula for adding complex numbers?
+(a + bi) + (c + di) = (a + c) + (b + d)i
What is the formula for subtracting complex numbers?
+(a + bi) - (c + di) = (a - c) + (b - d)i
Can I multiply and divide complex numbers?
+Yes, you can multiply and divide complex numbers. However, these operations are not covered in this guide.
Related Terms:
- Multiplying complex numbers Worksheet pdf
- Simplify Complex Numbers Worksheet
