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Adding Complex Numbers: (7+3i) + (-8+9i)
This article will guide you through the process of adding two complex numbers: (7+3i) + (-8+9i).
Understanding Complex Numbers
Complex numbers are numbers 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.
Adding Complex Numbers
To add complex numbers, we simply add their real and imaginary components separately.
Here's how to add (7+3i) + (-8+9i):
- Combine the real parts: 7 + (-8) = -1
- Combine the imaginary parts: 3i + 9i = 12i
Therefore, the sum of (7+3i) + (-8+9i) is -1 + 12i.
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 graphically involves connecting the points representing each number and drawing a vector from the origin to the endpoint of the second vector.
Conclusion
Adding complex numbers is a straightforward process. By combining the real and imaginary components separately, we can easily determine the sum of two complex numbers.