%2B(3-2i).jpeg "(5+2i)+(3-2i)")
Adding Complex Numbers: (5 + 2i) + (3 - 2i)
This article will guide you through the process of adding two complex numbers: (5 + 2i) and (3 - 2i).
Understanding Complex Numbers
Complex numbers are numbers that consist of two parts: a real part and an imaginary part. The imaginary part is denoted by the letter 'i', where i² = -1.
Adding Complex Numbers
Adding complex numbers is straightforward. We simply add the real parts together and the imaginary parts together separately.
Step 1: Identify the real and imaginary parts of each number:
- (5 + 2i) has a real part of 5 and an imaginary part of 2i.
- (3 - 2i) has a real part of 3 and an imaginary part of -2i.
Step 2: Add the real parts together:
- 5 + 3 = 8
Step 3: Add the imaginary parts together:
- 2i + (-2i) = 0
Step 4: Combine the results:
- 8 + 0 = 8
Therefore, (5 + 2i) + (3 - 2i) = 8.
Important Note: The imaginary part cancels out in this specific example. This is not always the case when adding complex numbers.
Conclusion
Adding complex numbers is a simple process involving combining the real and imaginary parts separately. This allows us to manipulate and work with complex numbers effectively in various mathematical contexts.