Multiplying Complex Numbers: (9  4i)(2 + 9i)
This article will guide you through the process of multiplying two complex numbers, specifically (9  4i)(2 + 9i).
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, similar to multiplying binomials in algebra:

Expand the product: (9  4i)(2 + 9i) = 9(2 + 9i)  4i(2 + 9i)

Distribute: = 18 + 81i  8i  36i²

Simplify using i² = 1: = 18 + 81i  8i + 36

Combine real and imaginary terms: = (18 + 36) + (81  8)i

Final result: = 54 + 73i
Conclusion
Therefore, the product of (9  4i)(2 + 9i) is 54 + 73i. This process demonstrates how to multiply complex numbers and arrive at a simplified complex number expression.