(5-8i)-2i(2-3i)

Jasonbradley

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Jun 16, 2024

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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

1. Distribute the -2i: (5 - 8i) - 2i(2 - 3i) = (5 - 8i) + (-4i + 6i²)

2. Substitute i² with -1: (5 - 8i) + (-4i + 6i²) = (5 - 8i) + (-4i - 6)

3. Combine like terms: (5 - 8i) + (-4i - 6) = -1 - 12i

Final Result

Therefore, the simplified form of (5-8i) - 2i(2-3i) is -1 - 12i.