# complex analysis – maximum product of distances of a point and vertices of equilateral triangle

If $$ABC$$ is an equilateral triangle. $$P$$ is a variable point inside the triangle or on its sides. We need to find the maximum product of $$AP cdot BP cdot CP$$.

This question is in a Complex Analysis homework.
I don’t know how can I use the complex analysis (maybe, maximum modulus theorem ) to find the maximum product.