Problem
Let 𝑧̅ denote the complex conjugate of a complex number z. If z is a non-zero complex number for which both real and imaginary parts of (𝑧̅)2 + 1/z2 are integers, then which of the following is / are possible value(s) of |z|?
A ((43 + 3√205)/4)1/4
B ((7 + √33)/4)1/4
C ((9 + √65)/4)1/4
D ((7 + √13)/6)1/4