Multiplying Complex Numbers: (1 + 4i) * (4  3i)
This article will demonstrate how to multiply two complex numbers: (1 + 4i) * (4  3i).
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 (i² = 1).
Multiplication Process
To multiply two complex numbers, we use the distributive property (or FOIL method) just like multiplying binomials in algebra.

Distribute: Multiply each term in the first complex number by each term in the second complex number.
(1 + 4i) * (4  3i) = (1 * 4) + (1 * 3i) + (4i * 4) + (4i * 3i)

Simplify: Combine real and imaginary terms.
= 4 + 3i + 16i  12i²

Substitute i² = 1:
= 4 + 3i + 16i + 12

Combine Like Terms:
= 8 + 19i
Result
Therefore, the product of (1 + 4i) and (4  3i) is 8 + 19i.