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Adding Complex Numbers: (3-4i) + (2+5i)
This article will guide you through the process of adding complex numbers, specifically the example of (3-4i) + (2+5i).
Understanding Complex Numbers
Complex numbers are numbers that consist of two parts: a real part and an imaginary part. They are written in the form a + bi, where:
- a represents the real part.
- b represents the imaginary part.
- i is the imaginary unit, defined as the square root of -1 (i² = -1).
Adding Complex Numbers
To add complex numbers, we simply add the real parts and the imaginary parts separately.
Step 1: Identify the real and imaginary parts of each complex number.
In our example:
- (3-4i): Real part = 3, Imaginary part = -4
- (2+5i): Real part = 2, Imaginary part = 5
Step 2: Add the real parts together.
3 + 2 = 5
Step 3: Add the imaginary parts together.
-4 + 5 = 1
Step 4: Combine the results from steps 2 and 3 to form the final complex number.
Therefore, (3-4i) + (2+5i) = 5 + i.
Conclusion
Adding complex numbers is a straightforward process that involves combining the real and imaginary parts separately. Remember, the imaginary unit 'i' remains constant throughout the operation. By following these steps, you can confidently add any pair of complex numbers.