Hello,
I am not able to solve this question so can anyone please help me. The question as it is -

Let z1 and z2 be the roots of the equation z^2 + pz + q = 0, where p and q may be complex number. Let A and B represent z1 and z2 in the complex plane. If angle AOB=a not equal to 0 and OA=OB,where O is the origin then p^2 =

- 4qcos^2 (a/2)
- 2qcos^2(a)
- qcos^2 (a/4)

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TopNewestAnswer is 1.

\(By\quad rotation\quad ,\\ { z }_{ 1 }={ z }_{ 2 }{ e }^{ ia }\\ From\quad quadratic\quad ,\\ { z }_{ 1 }{ z }_{ 2 }=q\\ Eliminating\quad we\quad get\quad ,\\ { z }_{ 1 }=\sqrt { q } { e }^{ -\cfrac { ia }{ 2 } }\\ { z }_{ 2 }=\sqrt { q } { e }^{ \frac { ia }{ 2 } }\\ Sum\quad of\quad roots\quad is\quad p,\\ Hence\quad ,\\ { p }^{ 2 }=4q\cos ^{ 2 }{ \frac { a }{ 2 } } \) – Rohit Shah · 2 years ago

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– Tarun Singh · 2 years ago

Thankyou very much for the solution.Log in to reply