Multiplying Complex Numbers: (86i)(44i)
This article will demonstrate how to multiply two complex numbers: (86i) and (44i).
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 (also known as FOIL method) like we do with binomials. Here's the breakdown:

Distribute: Multiply each term in the first complex number by each term in the second complex number. (8  6i)(4  4i) = (8)(4) + (8)(4i) + (6i)(4) + (6i)(4i)

Simplify: Perform the multiplications and combine like terms. = 32  32i + 24i + 24i²

Substitute i² = 1: Replace any occurrences of i² with 1. = 32  32i + 24i + 24(1)

Combine Real and Imaginary Parts: Group the real terms and the imaginary terms. = (32  24) + (32 + 24)i

Final Result: Simplify the expression. = 56  8i
Conclusion
Therefore, the product of (86i) and (44i) is 56  8i.