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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