(1/3+7/3i)+(4+1/3i)-(-4/3+i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of simplifying the following complex number expression:

(1/3 + 7/3i) + (4 + 1/3i) - (-4/3 + i)

Understanding Complex Numbers

Complex numbers are numbers that consist of two parts: a real part and an imaginary part. The imaginary part is denoted by the imaginary unit i, where i² = -1.

Simplifying the Expression

To simplify the given expression, we follow these steps:

1. Distribute the negative sign:

   (1/3 + 7/3i) + (4 + 1/3i) + (4/3 - i)

2. Combine real and imaginary terms:

   (1/3 + 4 + 4/3) + (7/3i + 1/3i - i)

3. Simplify the real and imaginary parts separately:

   (9/3) + (5/3i - i)

   3 + (2/3)i

Therefore, the simplified form of the given complex number expression is 3 + (2/3)i.

Key Points to Remember

• When adding or subtracting complex numbers, we add/subtract the real parts and the imaginary parts separately.
• The imaginary unit i is treated as a variable, and we can perform operations like addition, subtraction, and multiplication on it.
• Remember that i² = -1.

Conclusion

Simplifying complex number expressions involves combining the real and imaginary terms separately. By understanding the basic principles of complex numbers, we can efficiently manipulate and simplify these expressions.