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Adding Complex Numbers: (8 + 2i) + (-2 + 4i)
This article will guide you through the process of adding two complex numbers: (8 + 2i) + (-2 + 4i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where:
- a is the real part, a real number.
- b is the imaginary part, a real number.
- i is the imaginary unit, where i² = -1.
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 + 2i) has a real part of 8 and an imaginary part of 2.
(-2 + 4i) has a real part of -2 and an imaginary part of 4.
Step 2: Add the real parts: 8 + (-2) = 6
Step 3: Add the imaginary parts: 2 + 4 = 6
Step 4: Combine the results: 6 + 6i
Therefore, (8 + 2i) + (-2 + 4i) = 6 + 6i.
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 the vector sum of the two complex numbers on the complex plane.