\( 1 \leftarrow \quad \begin{array}{l}\text { Multiply } \\ (6+3 i)(9+3 i)\end{array} \)

To multiply the complex numbers \( (6 + 3i)(9 + 3i) \), you can use the distributive property (also known as the FOIL method for binomials). First, calculate the real and imaginary parts separately: 1. **Real Part:** \( 6 \cdot 9 = 54 \) 2. **Outer:** \( 6 \cdot 3i = 18i \) 3. **Inner:** \( 3i \cdot 9 = 27i \) 4. **Imaginary Part:** \( 3i \cdot 3i = 9i^2 \) (remember that \( i^2 = -1 \), so this becomes \(-9\)) Now combine these results: - Real part: \( 54 - 9 = 45 \) - Imaginary part: \( 18i + 27i = 45i \) Therefore, the product is \( 45 + 45i \). Now you can impress your friends with your complex multiplication skills!