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Complex Numbers question

2022 · Shift 2 · Q29

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2022 · Shift 2 · Q29

Complex Numbers question

2022 · Shift 2 · Q29

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −2

Let

\bar{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

(\bar{z})^{2}+\frac{1}{z^{2}}

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

|z|

?

A
$\left(\frac{43+3 \sqrt{205}}{2}\right)^{\frac{1}{4}}$
B
$\left(\frac{7+\sqrt{33}}{4}\right)^{\frac{1}{4}}$
C
$\left(\frac{9+\sqrt{65}}{4}\right)^{\frac{1}{4}}$
D
$\left(\frac{7+\sqrt{13}}{6}\right)^{\frac{1}{4}}$

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