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Let's multiply the two complex numbers \((-3 + 2i)(-4 + 4i)\) step by step.

### Step 1: Expand the product using distributive property
\[
(-3 + 2i)(-4 + 4i) = (-3)(-4) + (-3)(4i) + (2i)(-4) + (2i)(4i)
\]

### Step 2: Compute individual terms
- \((-3)(-4) = 12\)
- \((-3)(4i) = -12i\)
- \((2i)(-4) = -8i\)
- \((2i)(4i) = 8i^2\)

### Step 3: Use \(i^2 = -1\)
\[
8i^2 = 8(-1) = -8
\]

### Step 4: Combine real and imaginary parts
Now, group the real and imaginary terms:
\[
12 - 8 + (-12i - 8i)
\]
\[
(12 - 8) + (-12i - 8i) = 4 - 20i
\]

### Final Answer
The product of \((-3 + 2i)(-4 + 4i)\) is:
\[
4 - 20i
\]

Thus, the answer in standard form is:
\[
4 - 20i
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you add two complex numbers?
2. What is the geometric meaning of multiplying complex numbers?
3. What happens when you multiply a complex number by its conjugate?
4. How do you convert a complex number from rectangular to polar form?
5. What are the rules for dividing two complex numbers?

**Tip:** When multiplying complex numbers, always remember to simplify \(i^2\) to \(-1\).

Multiply (-3 + 2i)(-4 + 4i) and write the answer as a complex number in standard form.

Explore how to multiply the complex numbers (-3 + 2i) and (-4 + 4i) step by step. This solution covers the distributive property, handling imaginary units, and combining real and imaginary parts to write the answer in standard form, ideal for students in Grades 9-12.

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