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

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (-2 + 2i)(5 + 5i)

This article will guide you through the process of multiplying two complex numbers: (-2 + 2i) and (5 + 5i).

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 (i² = -1).

Multiplication Process

To multiply complex numbers, we use the distributive property, just like with regular binomials. This means we multiply each term of the first complex number by each term of the second complex number.

1. Expand the product: (-2 + 2i)(5 + 5i) = (-2 * 5) + (-2 * 5i) + (2i * 5) + (2i * 5i)

2. Simplify: = -10 - 10i + 10i + 10i²

3. Substitute i² = -1: = -10 - 10i + 10i + 10(-1)

4. Combine like terms: = -10 - 10 + 10i - 10i

5. Final result: = -20

Conclusion

Therefore, the product of (-2 + 2i) and (5 + 5i) is -20. Notice that the result is a purely real number, even though we started with complex numbers. This demonstrates that the multiplication of complex numbers can lead to different types of results.