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Adding Complex Numbers: (3 + 2i) + (4 - 5i)
This article explores the addition of complex numbers, specifically the operation (3 + 2i) + (4 - 5i).
Understanding Complex Numbers
Complex numbers are numbers that extend the real number system by including the imaginary unit 'i', where i² = -1. They are expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit.
Addition of Complex Numbers
Adding complex numbers is straightforward. We simply add the real parts and the imaginary parts separately.
To add (3 + 2i) + (4 - 5i):
- Combine the real parts: 3 + 4 = 7
- Combine the imaginary parts: 2i - 5i = -3i
Therefore, (3 + 2i) + (4 - 5i) = 7 - 3i.
Visualizing Complex Numbers
Complex numbers can be visualized on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. Adding complex numbers geometrically involves connecting the points representing the two complex numbers and drawing the diagonal of the parallelogram formed. This diagonal represents the sum of the two complex numbers.
Conclusion
Adding complex numbers involves a simple process of combining the real and imaginary parts separately. This operation is essential in various mathematical applications, including electrical engineering, quantum mechanics, and signal processing.