-2i(2-3i)-in-standard-form.jpeg "(5-8i)-2i(2-3i) In Standard Form")
Simplifying Complex Numbers: (5 - 8i) - 2i(2 - 3i)
This article will demonstrate the process of simplifying the complex expression (5 - 8i) - 2i(2 - 3i) and presenting it in standard form (a + bi).
Understanding the Steps
- Distribute: Start by distributing the -2i across the second set of parentheses.
- Simplify: Combine like terms (real numbers with real numbers, and imaginary numbers with imaginary numbers).
- Standard Form: Express the final result in the standard form of a complex number (a + bi).
Simplifying the Expression
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Distribute: (5 - 8i) - 2i(2 - 3i) = 5 - 8i - 4i + 6i²
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Simplify: Remember that i² = -1. Substitute this value: 5 - 8i - 4i + 6(-1) = 5 - 8i - 4i - 6 Combining like terms: (5 - 6) + (-8 - 4)i = -1 - 12i
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Standard Form: The simplified expression in standard form is -1 - 12i.
Conclusion
By applying the rules of complex number arithmetic, we have successfully simplified the expression (5 - 8i) - 2i(2 - 3i) to its standard form, -1 - 12i.