Multiplying Complex Numbers: (7 + 2i)(9  6i)
This article will demonstrate how to multiply two complex numbers: (7 + 2i) and (9  6i).
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 how we multiply binomials:

Expand the product: (7 + 2i)(9  6i) = 7(9  6i) + 2i(9  6i)

Distribute: = 63  42i + 18i  12i²

Simplify by substituting i² with 1: = 63  42i + 18i + 12

Combine real and imaginary terms: = (63 + 12) + (42 + 18)i

Final Result: = 75  24i
Therefore, the product of (7 + 2i) and (9  6i) is 75  24i.
Conclusion
Multiplying complex numbers involves applying the distributive property and simplifying by substituting i² with 1. This process results in a new complex number, expressed in the standard form a + bi.