(2-3i).jpeg "(3-3i)(2-3i)")
Multiplying Complex Numbers: (3 - 3i)(2 - 3i)
This article will guide you through the process of multiplying two complex numbers, specifically (3 - 3i)(2 - 3i). We will use the distributive property and the fact that i² = -1.
Step 1: Apply the Distributive Property
We distribute each term in the first complex number to both terms in the second complex number:
(3 - 3i)(2 - 3i) = 3(2 - 3i) - 3i(2 - 3i)
Step 2: Simplify
Now we multiply the terms:
= 6 - 9i - 6i + 9i²
Step 3: Substitute i² with -1
Remember that i² = -1, so we substitute it into the equation:
= 6 - 9i - 6i + 9(-1)
Step 4: Combine Real and Imaginary Terms
Combine the real terms and the imaginary terms separately:
= (6 - 9) + (-9 - 6)i
Step 5: Simplify the Result
Simplify to get the final answer:
= -3 - 15i
Therefore, the product of (3 - 3i) and (2 - 3i) is -3 - 15i.