Let z(1) and z(2) be roots of the equati...

Let `z_(1) and z_(2)` be roots of the equation `z^(2) + pz+q= 0`, where the coefficients p and q may be complex numbers. Let A and B represent `z_(1) and z_(2)`, respectively, in the complex plane. If `angleAOB= theta ne 0 and OA= OB`, where O is the origin, then prove that `p^(2)=4q "cos"^(2) (theta)/(2)`.

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