Prove that angles are equal using complex numbers

Question

that in triangle $\Delta ABC$, where $D$ is a point on side $BC$, $E$ is a point on side $AB$, $BD=AC$, $AD=AE$ and $AB^2=AC\cdot BC$: angle $BAD$ is equal to angle $CEA$. This problem can be quite easily solved using elementary geometry, but I'm interested in other, more interesting methods, like using complex numbers. Or analytic geometry. If it is possible this way.