Simplifying Complex Number Multiplication
This article explores the simplification of the complex number expression (1  i)(2 + 3i)(4  4i).
Understanding Complex Numbers
Complex numbers are numbers of the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of 1 (i.e., i² = 1).
StepbyStep Simplification
To simplify the given expression, we'll multiply the complex numbers stepbystep:

Multiply the first two factors: (1  i)(2 + 3i) = (1 * 2) + (1 * 3i) + (i * 2) + (i * 3i) = 2 + 3i  2i  3i² = 2 + i + 3 (since i² = 1) = 5 + i

Multiply the result from step 1 by the third factor: (5 + i)(4  4i) = (5 * 4) + (5 * 4i) + (i * 4) + (i * 4i) = 20  20i + 4i  4i² = 20  16i + 4 (since i² = 1) = 24  16i
Conclusion
Therefore, the simplified form of the complex number expression (1  i)(2 + 3i)(4  4i) is 24  16i.