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Adding Complex Numbers: (11-7i) + (2-5i)
This article will guide you through adding the complex numbers (11 - 7i) and (2 - 5i).
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
Adding complex numbers is straightforward. You simply add the real parts and the imaginary parts separately.
Step 1: Identify the Real and Imaginary Parts
- In (11 - 7i), the real part is 11 and the imaginary part is -7.
- In (2 - 5i), the real part is 2 and the imaginary part is -5.
Step 2: Add the Real Parts
11 + 2 = 13
Step 3: Add the Imaginary Parts
-7 + (-5) = -12
Step 4: Combine the Results
The sum of the complex numbers is the real part plus the imaginary part: (11 - 7i) + (2 - 5i) = 13 - 12i
Conclusion
Therefore, the sum of (11 - 7i) and (2 - 5i) is 13 - 12i.