Question 8
The complex numbers $z$ and $w$ satisfy the system $$
z + \frac{20\mathrm{i}}{w} = 5 + \mathrm{i},
$$ $$
w + \frac{12\mathrm{i}}{z} = -4 + 10\mathrm{i}.
$$
Find the smallest possible value of $|zw|^2.$
z + \frac{20\mathrm{i}}{w} = 5 + \mathrm{i},
$$ $$
w + \frac{12\mathrm{i}}{z} = -4 + 10\mathrm{i}.
$$
Find the smallest possible value of $|zw|^2.$