# Counting Zeros Under Unitary Action

Assume we have two polynomials $$f_1$$ and $$f_2$$ with Newton polytopes $$A_1 , A_2 \in \mathbb{Z}^2$$. Also suppose that coefficients of $$f_1$$ and $$f_2$$ are generic. Then we pick a unitary matrix $$Q$$ and act on $$f_2$$. How many common zeros $$f_1$$ and $$Q \circ f_2$$ have on $$(\mathbb{C}^{*})^{2}$$ ?