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Adding Complex Numbers: (21 + 2i) + (13 + 8i)
This article explores the addition of two complex numbers: (21 + 2i) and (13 + 8i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where:
- a and b are real numbers
- 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.
Applying the Concept to our Problem
Let's add (21 + 2i) and (13 + 8i):
- Combine the real parts: 21 + 13 = 34
- Combine the imaginary parts: 2i + 8i = 10i
Therefore, the sum of (21 + 2i) and (13 + 8i) is 34 + 10i.
Visualizing Complex Numbers
Complex numbers can be visualized on a complex plane. The real part is represented on the horizontal axis (x-axis) and the imaginary part on the vertical axis (y-axis). Adding complex numbers can be visualized as finding the resultant vector by adding the corresponding components.
Conclusion
Adding complex numbers is a straightforward process involving adding the real parts and the imaginary parts separately. This operation, like other operations with complex numbers, has a clear geometric interpretation on the complex plane, providing a deeper understanding of their behavior.