We are given a regular pentagon \(A_1A_2A_3A_4A_5\) in the Cartesian plane centered at the origin with \(A_1 = (1,0)\). Let \(P = (1, \sqrt{3})\).

Denote \(z = \displaystyle \prod_{i=1}^5 m(PA_i)\), where \(m(AB)\) denotes the length of segment \(AB\).

Submit your answer as \(z^2\).

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