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Adding Complex Numbers: (8 + 3i) + (-6 - 12i)
This article will demonstrate how to add two complex numbers: (8 + 3i) + (-6 - 12i).
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.
- Real Part: The real part of a complex number is the constant term (a).
- Imaginary Part: The imaginary part of a complex number is the coefficient of i (b).
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:
- (8 + 3i): Real part = 8, Imaginary part = 3
- (-6 - 12i): Real part = -6, Imaginary part = -12
Step 2: Add the real parts: 8 + (-6) = 2
Step 3: Add the imaginary parts: 3 + (-12) = -9
Step 4: Combine the results: 2 + (-9)i = 2 - 9i