-%E2%80%93-(3-%E2%80%93-10i-)-%3D-11-%2B-2i-%E2%80%93-3-%E2%80%93-10i-%3D-(11-%E2%80%93-3)-%2B-(2i-%E2%80%93-10i)-%3D-8-%E2%80%93-8i.jpeg "(11 + 2i ) – (3 – 10i ) = 11 + 2i – 3 – 10i = (11 – 3) + (2i – 10i) = 8 – 8i")
Simplifying Complex Numbers: A Step-by-Step Guide
This article will provide a clear explanation of how to simplify the expression (11 + 2i) – (3 – 10i), demonstrating the process step by step.
Understanding Complex Numbers
Complex numbers are a fundamental concept in mathematics, represented in the form a + bi, where:
- a is the real part
- b is the imaginary part
- i is the imaginary unit, defined as the square root of -1 (i.e., i² = -1)
Simplifying the Expression
Let's break down the simplification of (11 + 2i) – (3 – 10i):
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Distribute the negative sign: The first step is to distribute the negative sign in front of the second complex number: (11 + 2i) – (3 – 10i) = 11 + 2i – 3 + 10i
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Combine real and imaginary terms: Next, we group the real terms together and the imaginary terms together: (11 – 3) + (2i + 10i)
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Simplify: Finally, we perform the addition/subtraction for both the real and imaginary parts: 8 – 8i
Conclusion
By following these simple steps, we have successfully simplified the expression (11 + 2i) – (3 – 10i) to 8 – 8i. This process demonstrates the fundamental operations of addition, subtraction, and combining like terms within the realm of complex numbers.