The complex number associated with the vertices `A, B, C` of `DeltaABC` are `e^(i theta),omega,bar omega`, respectively [ where `omega,bar omega` are the com plex cube roots of unity and `cos theta > Re(omega)`], then the complex number of the point where angle bisector of A meets cumcircle of the triangle, is

Options

A. `e^(itheta)`
B. `e^(-itheta)`
C. `omega,baromega`
D. `omega+baromega`

Answer

D

Explanation

Clerly,

`/_ DOB = /_COD= A`
`rArr z = omega e^(1//4) and baromega = ze^(1//4)" "("Applying rotation about O")`
`rArr z^(2) = omega baromega =1`
`rArr z = -1`
(As A and D are on opposite sides of BC)