**Multiply and simplify the following complex numbers:**

\[(\pink{2-2i}) \cdot (\blue{4-4i})\]

To multiply and simplify the complex numbers \((2 - 2i) \cdot (4 - 4i)\), we'll use the distributive property (FOIL method).

Let's go through the steps:

1. **First**: Multiply the first terms from each binomial:
   \[
   2 \cdot 4 = 8
   \]

2. **Outer**: Multiply the outer terms:
   \[
   2 \cdot (-4i) = -8i
   \]

3. **Inner**: Multiply the inner terms:
   \[
   -2i \cdot 4 = -8i
   \]

4. **Last**: Multiply the last terms:
   \[
   -2i \cdot (-4i) = 8i^2
   \]

Recall that \(i^2 = -1\), so:
\[
8i^2 = 8(-1) = -8
\]

Now, add up all the terms:
\[
8 - 8i - 8i - 8
\]

Combine the real and imaginary parts:
\[
(8 - 8) + (-8i - 8i) = 0 - 16i
\]

Thus, the simplified result of multiplying \((2 - 2i) \cdot (4 - 4i)\) is:
\[
\boxed{-16i}
\]

Would you like to see further details or have any questions?

Here are 5 related questions:
1. What happens when you square a complex number?
2. How do you divide complex numbers?
3. How do you determine if two complex numbers are equal?
4. What are the real and imaginary parts of a complex number?
5. How do you graph a complex number on the complex plane?

**Tip:** When multiplying complex numbers, always simplify \(i^2\) to \(-1\) to get the correct real and imaginary components.

Learn how to multiply and simplify the complex numbers (2 - 2i) * (4 - 4i) with a step-by-step solution. This problem involves basic operations with complex numbers, including the distributive property and simplifying terms with the imaginary unit (i). Suitable for advanced high school students in Grades 11-12.

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