1.        (3 + 3*i*)(-5 – 2*i*)

*Show your work below:*

Let's compute the product of the two complex numbers \((3 + 3i)(-5 - 2i)\).

### Step-by-step solution:

1. **Distribute using the distributive property (FOIL method):**
   \[
   (3 + 3i)(-5 - 2i) = 3(-5) + 3(-2i) + 3i(-5) + 3i(-2i)
   \]
   Breaking it down:
   - \( 3(-5) = -15 \)
   - \( 3(-2i) = -6i \)
   - \( 3i(-5) = -15i \)
   - \( 3i(-2i) = -6i^2 \)

2. **Simplify the terms:**
   Recall that \( i^2 = -1 \), so:
   \[
   3i(-2i) = -6(-1) = 6
   \]
   Now, substitute back into the expression:
   \[
   -15 - 6i - 15i + 6
   \]

3. **Combine like terms:**
   - Real part: \( -15 + 6 = -9 \)
   - Imaginary part: \( -6i - 15i = -21i \)

4. **Final answer:**
   \[
   (3 + 3i)(-5 - 2i) = -9 - 21i
   \]

Would you like more details or have any questions?

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Here are 5 related questions you might explore:
1. What happens when two purely imaginary numbers are multiplied?
2. How do you calculate the magnitude of a complex number?
3. What is the geometric interpretation of multiplying complex numbers?
4. How do you find the conjugate of a complex number?
5. How do you divide two complex numbers?

**Tip:** When multiplying complex numbers, always apply the distributive property (FOIL) and simplify carefully using \(i^2 = -1\).

Learn how to multiply complex numbers with this detailed solution of (3 + 3i)(-5 - 2i). Using the FOIL method, we simplify the product and apply the properties of imaginary numbers. Suitable for students in Grades 10-12.

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