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