If $z = 3 - 4i$ and $\bar{z}$ is its conjugate, find $z\bar{z}$.

$z\bar{z} = (3 - 4i)(3 + 4i) = 9 - 16i^2 = 9 + 16 = 25$, which is always $|z|^2$. Treating $i^2$ as $1$ gives $-7$, and $5$ is the modulus rather than its square.