# Complex Vectors?

Geometry Level 4

Let $$ABC$$ Be an isosceles triangle in the argand plane. Let $$x,y$$ and $$z$$ represent complex numbers corresponding to vertices $$A,B$$ and $$C$$ respectively. It is given that $$AC = BC$$ and the equal angles of the triangle are 30 degrees .Let $$p$$ represent the complex number corresponding to incentre of the triangle $$ABC$$. Then find the value of $$q$$ if $$(y-x)(z-x) = q (p-x)^2$$.

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