The given expression is $(3 + 4i)(2 - 2i)$, where $i$ represents the imaginary unit.

Let's multiply these two complex numbers using the distributive property (FOIL method):

$(3 + 4i)(2 - 2i)$

Step-by-step multiplication:

1. First, multiply the first terms: $3 \times 2 = 6$
2. Multiply the outer terms: $3 \times -2i = -6i$
3. Multiply the inner terms: $4i \times 2 = 8i$
4. Multiply the last terms: $4i \times -2i = -8i^2$ Since $i^2 = -1$, this becomes: $-8i^2 = -8(-1) = 8$

Now, combine all these results:

$6 - 6i + 8i + 8$

Combine like terms: $(6 + 8) + (-6i + 8i) = 14 + 2i$

Final result:

$(3 + 4i)(2 - 2i) = 14 + 2i$

Would you like more details on any part of this? Here are five related questions for further exploration:

1. What is the general formula for multiplying two complex numbers?
2. How does $i^2 = -1$ affect complex number calculations?
3. Can you represent the result $14 + 2i$ on the complex plane?
4. What is the geometric interpretation of multiplying complex numbers?
5. How would you divide two complex numbers?

Tip: Always remember that when multiplying two complex numbers, use the FOIL method and simplify using the fact that $i^2 = -1$.