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Subtracting Complex Numbers: (-3 + 8i) - (1 + 8i)
This article will guide you through the process of subtracting two complex numbers: (-3 + 8i) - (1 + 8i).
Understanding Complex Numbers
Complex numbers are numbers that consist of a real part and an imaginary part. They are written in the form a + bi, where 'a' represents the real part and 'b' represents the imaginary part, and 'i' is the imaginary unit (where i² = -1).
Subtracting Complex Numbers
To subtract complex numbers, we simply subtract the real parts and the imaginary parts separately.
Step 1: Distribute the Negative Sign First, we need to distribute the negative sign in front of the second complex number:
(-3 + 8i) - (1 + 8i) = -3 + 8i - 1 - 8i
Step 2: Combine Real and Imaginary Terms Now, group the real terms and the imaginary terms together:
(-3 - 1) + (8i - 8i)
Step 3: Simplify Finally, simplify the expression:
-4 + 0i
Therefore, (-3 + 8i) - (1 + 8i) = -4
Conclusion
Subtracting complex numbers is quite straightforward. We simply treat the real and imaginary parts separately, just like we do with regular numbers. In this case, the imaginary parts canceled each other out, leaving us with a purely real number as the result.