(5+2i)(1+3i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (5 + 2i)(1 + 3i)

This article will explore the multiplication of two complex numbers: (5 + 2i) and (1 + 3i).

Understanding Complex Numbers

Complex numbers are numbers that consist of a real part and an imaginary part. The imaginary part is represented by the symbol "i", where i² = -1.

Multiplication Process

To multiply complex numbers, we use the distributive property, similar to multiplying binomials.

1. Distribute the first term: (5 + 2i)(1 + 3i) = 5(1 + 3i) + 2i(1 + 3i)

2. Expand the products: = 5 + 15i + 2i + 6i²

3. Simplify using i² = -1: = 5 + 15i + 2i - 6

4. Combine real and imaginary terms: = (5 - 6) + (15 + 2)i

5. Final Result: = -1 + 17i

Conclusion

Therefore, the product of (5 + 2i) and (1 + 3i) is -1 + 17i. By understanding the distributive property and the definition of "i", we can effectively multiply complex numbers.