-2i(2-3i).jpeg "(5-8i)-2i(2-3i)")
Simplifying Complex Numbers: (5-8i) - 2i(2-3i)
This article will guide you through the process of simplifying the complex number expression: (5-8i) - 2i(2-3i).
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 (i.e., i² = -1).
Simplifying the Expression
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Distribute the -2i: (5 - 8i) - 2i(2 - 3i) = (5 - 8i) + (-4i + 6i²)
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Substitute i² with -1: (5 - 8i) + (-4i + 6i²) = (5 - 8i) + (-4i - 6)
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Combine like terms: (5 - 8i) + (-4i - 6) = -1 - 12i
Final Result
Therefore, the simplified form of (5-8i) - 2i(2-3i) is -1 - 12i.