(2-3i)(1-i)-(3-i)(3+i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Expressions

This article will guide you through the process of simplifying the complex expression: (2-3i)(1-i)-(3-i)(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, where i² = -1.

Simplifying the Expression

1. Expand the products:

   • (2-3i)(1-i) = 2 - 2i - 3i + 3i² = 2 - 5i + 3(-1) = -1 - 5i
   • (3-i)(3+i) = 9 + 3i - 3i - i² = 9 - (-1) = 10

2. Substitute the simplified products into the original expression:

   • (-1 - 5i) - 10

3. Combine like terms:

   • -11 - 5i

Final Answer

The simplified form of the expression (2-3i)(1-i)-(3-i)(3+i) is -11 - 5i.