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Let bar(z) denote the complex conjugate ...

Let `bar(z)` denote the complex conjugate of a complex number ?. If ? is a non-zero complex number for which both real and imaginary parts of `(bar(z))^(2)+1/(z^(2))`
are integers, then which of the following is/are possible value(s) of |z| ?

A

`((43 +3sqrt(205))/2)^(1/4)`

B

`((7+sqrt(3))/4)^(1/4)`

C

`((9+sqrt(65))/4)^(1/4)`

D

`((7+sqrt(13))/6)^(1/4)`

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