Multiplying Complex Numbers: (3  i) * (3 + i)
This article will demonstrate how to multiply two complex numbers, specifically (3  i) * (3 + i).
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 follow a similar process to multiplying binomials:
 Distribute: Multiply each term in the first complex number by each term in the second complex number.
 Simplify: Combine like terms, remembering that i² = 1.
Applying the Process
Let's multiply (3  i) * (3 + i):

Distribute:
 3 * 3 = 9
 3 * i = 3i
 i * 3 = 3i
 i * i = i²

Simplify:
 9  3i  3i  i²
 9  6i  (1) (Since i² = 1)
 9 + 1  6i
 8  6i
Result
Therefore, the product of (3  i) * (3 + i) is 8  6i.