JEE Main 2025 (Online) 23rd January Evening ShiftQuestion 1
The number of complex numbers $z$, satisfying $|z|=1$ and $\left|\frac{z}{\bar z}+\frac{\bar z}{z}\right|=1$, is :
Complex Numbers
Solution
With $z=e^{i\theta}$, $\frac z{\bar z}+\frac{\bar z}z=2\cos2\theta$, so $\cos2\theta=\pm\frac12$. In $[0,2\pi)$ each sign gives $4$ values of $\theta$, total $8$.