Question

Let the complex numbers `z_1`, `z_2` and `z_3` represent the vertices A, B and C of a triangle ABC respectively, which is inscribed in the circle of radius unity and centre at origin.The internal bisector of the angle A meets the circumcircle again at the point D, Which is represented by the complex number `z_4` and altitude from A to BC meets the circumcircle at E. given by `z_5`. Then `arg([z_2z_3]/z_4^2)` is equal to

Answer 1

Arc(BD)=Arc(CD)
`Z_2/Z_4=e^(1(b-d))`
`Z_3/Z_4=e^(i(c-d))`
`Z_4/Z_3=e^(i(d-c))=e^(i(b-d))`
`Z_4^2=Z_2Z_3`
`(Z_2Z_3)/Z_4^2=1`
`arg((Z_2Z_3)/Z_4^2)=1`.