1. **State the problem:** Multiply and simplify the complex numbers $(-2 + 2i)$ and $(5 + 5i)$. 2. **Recall the formula:** To multiply two complex numbers $(a + bi)(c + di)$, use the distributive property: $$ (a + bi)(c + di) = ac + adi + bci + bdi^2 $$ Remember that $i^2 = -1$. 3. **Apply the formula:** $$ (-2 + 2i)(5 + 5i) = (-2)(5) + (-2)(5i) + (2i)(5) + (2i)(5i) $$ 4. **Calculate each term:** $$ = -10 - 10i + 10i + 10i^2 $$ 5. **Simplify terms:** The $-10i$ and $+10i$ cancel out: $$ -10 + \cancel{-10i} + \cancel{10i} + 10i^2 = -10 + 10i^2 $$ 6. **Replace $i^2$ with $-1$:** $$ -10 + 10(-1) = -10 - 10 $$ 7. **Final simplification:** $$ -20 $$ **Answer:** The product simplifies to $-20$.