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.

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

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

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

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

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.