Simplifying Complex Numbers
This article will guide you through simplifying the complex number expression: (-2 - 4i) - (-5 - 2i) - (-5 - 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)
Simplifying the Expression
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Distribute the negative signs: (-2 - 4i) + (5 + 2i) + (5 + 5i)
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Combine real and imaginary terms separately: (-2 + 5 + 5) + (-4 + 2 + 5)i
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Simplify: 8 + 3i
Final Answer
Therefore, the simplified form of the expression (-2 - 4i) - (-5 - 2i) - (-5 - 5i) is 8 + 3i.