Multiplying Complex Numbers: (76i)(23i)
This article will guide you through the process of multiplying the complex numbers (76i) and (23i).
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 (or FOIL method) similar to multiplying binomials.

Expand the expression: (7  6i)(2  3i) = 7(2  3i)  6i(2  3i)

Distribute: = 14  21i  12i + 18i²

Substitute i² with 1: = 14  21i  12i + 18(1)

Combine real and imaginary terms: = (14  18) + (21  12)i

Simplify: = 4  33i
Conclusion
Therefore, the product of the complex numbers (76i) and (23i) is 4  33i.