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Adding Complex Numbers: (6-3i) + (5+4i)
This article will guide you through the process of adding two complex numbers: (6-3i) + (5+4i).
Understanding Complex Numbers
A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1 (i.e., i² = -1).
Adding Complex Numbers
To add complex numbers, we simply add the real parts and the imaginary parts separately.
Let's apply this to our problem:
(6 - 3i) + (5 + 4i)
- Combine the real parts: 6 + 5 = 11
- Combine the imaginary parts: -3i + 4i = i
Therefore, the sum of (6 - 3i) and (5 + 4i) is 11 + i.
Visual Representation
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 can be seen as vector addition on this plane.
In this case, (6-3i) and (5+4i) would be represented by vectors, and their sum (11+i) would be the resultant vector obtained by adding them.
Conclusion
Adding complex numbers is a straightforward process. By understanding the structure of complex numbers and applying the principle of adding real and imaginary parts separately, we can efficiently find the sum of any two complex numbers.