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

4 1 2 205 3 43 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +
4 1 4 33 7 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +
4 1 4 65 9 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +
4 1 6 13 7 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +

Correct answer: 4 1 2 205 3 43 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +

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