Question:

**Paragraph I (continued):** $z_1\bar{z}_2+z_2\bar{z}_1+z_2\bar{z}_3+z_3\bar{z}_2+z_1\bar{z}_3+z_3\bar{z}_1=$

Step-by-Step Solution

Key Concept: $\sum_{i\neq j}z_i\bar{z}_j=|z_1+z_2+z_3|^2-(|z_1|^2+|z_2|^2+|z_3|^2)=441-(27+132)=282$.

$\mathbf{282}$.

Correct Answer: 282