(2-3i)+(5+6i)+(-3-4i)

Jasonbradley

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Jun 16, 2024

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Adding Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of adding complex numbers, using the example of (2 - 3i) + (5 + 6i) + (-3 - 4i).

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 (i² = -1)

Adding Complex Numbers

Adding complex numbers is straightforward. We simply combine the real parts and the imaginary parts separately.

1. Identify the real and imaginary parts of each complex number:

   • (2 - 3i): Real part = 2, Imaginary part = -3
   • (5 + 6i): Real part = 5, Imaginary part = 6
   • (-3 - 4i): Real part = -3, Imaginary part = -4

2. Add the real parts: 2 + 5 + (-3) = 4

3. Add the imaginary parts: -3 + 6 + (-4) = -1

4. Combine the results: 4 - 1i

Therefore, the sum of (2 - 3i) + (5 + 6i) + (-3 - 4i) is 4 - i.

Key Points

• Adding complex numbers is essentially adding the real and imaginary components separately.
• Remember that i² = -1, which is crucial for simplifying expressions involving imaginary units.
• Complex number addition is commutative and associative, meaning the order of addition doesn't affect the result.

This example illustrates a simple method for adding complex numbers. By understanding the basic principles, you can easily manipulate and solve complex number problems.