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

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (5 + 3i)(2 - 5i)

This article will guide you through the process of multiplying two complex numbers: (5 + 3i) and (2 - 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 we do with binomials in algebra.

1. Expand the expression: (5 + 3i)(2 - 5i) = 5(2 - 5i) + 3i(2 - 5i)

2. Distribute: = 10 - 25i + 6i - 15i²

3. Simplify using i² = -1: = 10 - 25i + 6i + 15

4. Combine real and imaginary terms: = (10 + 15) + (-25 + 6)i

5. Final Result: = 25 - 19i

Conclusion

Therefore, the product of the complex numbers (5 + 3i) and (2 - 5i) is 25 - 19i.