Mathematics

Problem

In the complex plane, consider the parallelogram formed by the points

0, z, \frac{1}{z}

and

z + \frac{1}{z}

having area

\frac{12}{13}

square units and the real part of 'z' is positive. If the smallest possible value of

|z + \frac{1}{z}|

is 'p', then

\frac{13p^2}{4}

is - - -