Let `z_1 and z_2` be the root of the equation `z^2+pz+q=0` where the coefficient p and q may be complex numbers. Let A and B represent `z_1 and z_2` in the complex plane. If `/_AOB=alpha!=0 and 0 and OA=OB, where O` is the origin prove that `p^2=4qcos^2 (alpha/2)`

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 represnts z_1 and z_2 in the complex plane if angleAOB=alpha ne 0 and OA=OB where 0 is the origin prove that p^2=4qcos^2(alpha/2)

Let z_(1)andz_(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)andz_(2) in the complex plane. If angleAOB=alphane0andOA=OB, where O is the origin, prove that p^(2)=4cos^(2)(alpha//2).

Let z_1 \and\ z_2 be the roots of the equation z^2+p z+q=0, where the coefficients p \and \q may be complex numbers. Let A \and\ B represent z_1 \and\ z_2 in the complex plane, respectively. If /_A O B=theta!=0 \and \O A=O B ,\where\ O is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Let z_1 \and\ z_2 be the roots of the equation z^2+p z+q=0, where the coefficients p \and \q may be complex numbers. Let A \and\ B represent z_1 \and\ z_2 in the complex plane, respectively. If /_A O B=theta!=0 \and \O A=O B ,\where\ O is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Let z_1 \and\ z_2 be the roots of the equation z^2+p z+q=0, where the coefficients p \and \q may be complex numbers. Let A \and\ B represent z_1 \and\ z_2 in the complex plane, respectively. If /_A O B=theta!=0 \and \O A=O B ,\where\ O is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Let z_1a n dz_2 b be toots of the equation z^2+p z+q=0, where he coefficients pa n dq may be complex numbers. Let Aa n dB represent z_1a n dz_2 in the complex plane, respectively. If /_A O B=theta!=0a n dO A=O B ,w h e r eO is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Let z_1a n dz_2 b be toots of the equation z^2+p z+q=0, where he coefficients pa n dq may be complex numbers. Let Aa n dB represent z_1a n dz_2 in the complex plane, respectively. If /_A O B=theta!=0a n dO A=O B ,w h e r eO is the origin, prove that p^2=4q"cos"^2(theta//2)dot

z_(1) and z_(2) are the roots of the equation z^(2) -az + b=0 where |z_(1)|=|z_(2)|=1 and a,b are nonzero complex numbers, then