(7-6i)(2-3i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (7-6i)(2-3i)

This article will guide you through the process of multiplying the complex numbers (7-6i) and (2-3i).

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 (or FOIL method) similar to multiplying binomials.

1. Expand the expression: (7 - 6i)(2 - 3i) = 7(2 - 3i) - 6i(2 - 3i)

2. Distribute: = 14 - 21i - 12i + 18i²

3. Substitute i² with -1: = 14 - 21i - 12i + 18(-1)

4. Combine real and imaginary terms: = (14 - 18) + (-21 - 12)i

5. Simplify: = -4 - 33i

Conclusion

Therefore, the product of the complex numbers (7-6i) and (2-3i) is -4 - 33i.