Start with the expression
$$\sqrt[4]{81\mathrm{p}^3\mathrm{q}^5}$$
Simplify to
$$3q\sqrt[4]{\mathrm{p}^3q}$$
Assume $p = i, q = i$. Evaluate.
$$\sqrt[4]{81\mathrm{p}^3\mathrm{q}^5} = 3$$
$$3q\sqrt[4]{\mathrm{p}^3q} = 3i$$
Therefore, $3 = 3i, 1 = i$.
I suspect something related to absolute value, but can't figure it out at this moment.