Let $A$ and $B$ represent $z_1$ and $z_2$ in the Argand plane and $z_1, z_2$ be the roots of the equation…

Let $A$ and $B$ represent $z_1$ and $z_2$ in the Argand plane and $z_1, z_2$ be the roots of the equation $Z^2+p Z+q=0$, where $p, q$ are complex numbers. If $O$ is the origin, $O A=O B$ and $\lfloor A O B=\alpha$, then $p^2=$
  1. $2 q \cos \left(\frac{\alpha}{2}\right)$
  2. $4 q \cos \left(\frac{\alpha}{2}\right)$
  3. $4 q \cos ^2\left(\frac{\alpha}{2}\right)$
  4. $4 q^2 \cos ^2\left(\frac{\alpha}{2}\right)$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2017 (25 Apr Shift 1)

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