Here are the solutions for the first set of problems from your image (complex number multiplication):

7. $8(-2i)(-5 - 4i)$

   • Simplified: $-16i(-5 - 4i) = -80i - 64 = -64 + 80i$

8. $(2 - 2i)^2$

   • This expression can be expanded to $(2 - 2i)(2 - 2i) = 8i$

9. $(4i)(-2i)(-8 + 4i)$

   • Simplified: $(4i)(-2i)(-8 + 4i) = -64 + 32i$

10. $(-4 - 4i)(1 - 3i)$

    • Expanding: $(-4 - 4i)(1 - 3i) = -16 - 8i$

11. $(7 - 2i)(6 - 4i)$

    • Simplified to: $50 - 34i$

12. $(4 - 3i)(6 - 6i)$

    • Expanded: $42 - 18i$

Would you like detailed steps for each? Let me know!

Here are some related questions you could explore:

1. What is the general process for multiplying complex numbers?
2. How can we simplify expressions with powers of $i$?
3. What are the steps to divide complex numbers?
4. How does multiplying conjugates simplify complex expressions?
5. How can we express a complex number in polar form?

Tip: Always simplify powers of $i$ as $i^2 = -1$.