(5-2i)-2(3+i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: (5-2i)-2(3+i)

This article will guide you through simplifying the complex number expression (5-2i)-2(3+i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1 (i.e., i² = -1).

Simplifying the Expression

1. Distribute: Begin by distributing the -2 in the second term: (5-2i) -2(3+i) = 5 - 2i - 6 - 2i

2. Combine Real and Imaginary Terms: Group the real terms and the imaginary terms together: (5 - 6) + (-2 - 2)i

3. Simplify: Perform the arithmetic operations: -1 - 4i

Result

Therefore, the simplified form of (5-2i)-2(3+i) is -1 - 4i.