(2-3i)-(4-5i)+(-3+2i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: (2 - 3i) - (4 - 5i) + (-3 + 2i)

This article will walk you through the process of simplifying the complex number expression: (2 - 3i) - (4 - 5i) + (-3 + 2i)

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 negative signs: (2 - 3i) - (4 - 5i) + (-3 + 2i) = 2 - 3i - 4 + 5i - 3 + 2i

2. Combine real and imaginary terms separately: (2 - 4 - 3) + (-3 + 5 + 2)i

3. Simplify: -5 + 4i

The Final Answer

The simplified form of the complex number expression (2 - 3i) - (4 - 5i) + (-3 + 2i) is -5 + 4i.

Key Points to Remember

• Treat complex numbers like binomials: When adding or subtracting complex numbers, treat the real and imaginary parts separately.
• Simplify by combining like terms: Combine the real terms and the imaginary terms.
• Express the answer in the form a + bi: The final answer should be expressed in the standard complex number format.