Multiplying Complex Numbers: (3 + 3i) * (3  2i)
This article will guide you through multiplying the complex numbers (3 + 3i) and (3  2i).
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. The imaginary unit 'i' is defined as the square root of 1 (i² = 1).
Multiplication Process
To multiply complex numbers, we use the distributive property, just like we do with real numbers.

Expand the expression: (3 + 3i) * (3  2i) = (3 * 3) + (3 * 2i) + (3i * 3) + (3i * 2i)

Simplify: = 9 + 6i + 9i  6i²

Substitute i² with 1: = 9 + 6i + 9i  6(1)

Combine real and imaginary terms: = 9 + 6 + 6i + 9i

Final result: = 3 + 15i
Conclusion
Therefore, the product of (3 + 3i) and (3  2i) is 3 + 15i.
Remember, when multiplying complex numbers, you can treat them like binomials and use the distributive property. Also, always substitute i² with 1 to simplify the expression further.