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.

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

Distribute: = 10  25i + 6i  15i²

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

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

Final Result: = 25  19i
Conclusion
Therefore, the product of the complex numbers (5 + 3i) and (2  5i) is 25  19i.