QJEEM25Maa974: JEE Main 2025 Mathematics - Class 11 JEEM25Maa974 Solution: The number of complex numbers , satisfying and , is:

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QJEEM25Maa974: JEE Main 2025 Mathematics - Class 11 JEEM25Maa974 Solution: The number of complex numbers , satisfying and , is:

The number of complex numbers $z$ , satisfying $|z|=1$ and $\left|\frac{z}{\bar{z}}+\frac{\bar{z}}{z}\right|=1$ , is:

Multiple Choice Options

A 10
B 6
C 8
D 4

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Accepted Answer

$\begin{aligned} z = e^{i θ} \\ \frac{z}{\overset{―}{Z}} = e^{i 2 θ} \\ | \frac{z}{\overset{―}{Z}} + \frac{\overset{―}{z}}{z} | = 1 \Rightarrow | e^{i 2 θ} + e^{- 12 θ} | = 1 \Rightarrow | \cos 2 θ | = \frac{1}{2} \end{aligned}$

8 solution in $[0,2\pi)$

QJEEM25Maa974: JEE Main 2025 Mathematics - Class 11 JEEM25Maa974 Solution: The number of complex numbers , satisfying and , is:

Multiple Choice Options

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