Let \overline{z} 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 (\overline{z})^2+\frac{1}{z^2} are integers, then which of the following is/are possible value(s) of |z| ? [JEE Adv 2022 P2]

Correct Answer is : (43+3√2052)14

(\frac{43+3 \sqrt{205}{2})^{\frac{1}{4}}

(\frac{7+\sqrt{33}{4})^{\frac{1}{4}}

(\frac{9+\sqrt{65}{4})^{\frac{1}{4}}

(\frac{7+\sqrt{13}{6})^{\frac{1}{4}}

Complex Numbers

Section: Mathematics

Question : 7 of 36

Marks: +1, -0

Let z 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 (z)2+‌

are integers, then which of the following is/are possible value(s) of |z| ?

[JEE Adv 2022 P2]

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