(−3+3i)⋅(3−2i)

Jasonbradley

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Jun 17, 2024

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Multiplying Complex Numbers: (-3 + 3i) * (3 - 2i)

This article will guide you through multiplying the complex numbers (-3 + 3i) and (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, and 'i' is the imaginary unit. The imaginary unit 'i' is defined as the square root of -1 (i² = -1).

Multiplication Process

To multiply complex numbers, we use the distributive property, just like we do with real numbers.

1. Expand the expression: (-3 + 3i) * (3 - 2i) = (-3 * 3) + (-3 * -2i) + (3i * 3) + (3i * -2i)

2. Simplify: = -9 + 6i + 9i - 6i²

3. Substitute i² with -1: = -9 + 6i + 9i - 6(-1)

4. Combine real and imaginary terms: = -9 + 6 + 6i + 9i

5. Final result: = -3 + 15i

Conclusion

Therefore, the product of (-3 + 3i) and (3 - 2i) is -3 + 15i.

Remember, when multiplying complex numbers, you can treat them like binomials and use the distributive property. Also, always substitute i² with -1 to simplify the expression further.