To multiply the given complex numbers, we will use the distributive property of multiplication and simplify:

The expression is:
$(8 + 8i)(9 + i)$

Step-by-Step Solution:

1. Expand using the distributive property: $(8 + 8i)(9 + i) = 8 \cdot 9 + 8 \cdot i + 8i \cdot 9 + 8i \cdot i$

2. Compute each term:

   • $8 \cdot 9 = 72$
   • $8 \cdot i = 8i$
   • $8i \cdot 9 = 72i$
   • $8i \cdot i = 8i^2$

3. Substitute $i^2 = -1$ (by the property of imaginary numbers): $8i^2 = 8(-1) = -8$

4. Combine terms: $72 + 8i + 72i - 8$

   Simplify: $(72 - 8) + (8i + 72i) = 64 + 80i$

Final Answer:

$64 + 80i$

Would you like further clarification or details?

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Relative Questions:

1. What is the significance of $i^2 = -1$ in complex number operations?
2. How do you add or subtract two complex numbers?
3. How is the magnitude of a complex number calculated?
4. Can you explain how to divide complex numbers?
5. What are the practical applications of multiplying complex numbers?

Tip:

When multiplying complex numbers, always simplify $i^2$ to $-1$ early in the process to avoid errors.