Jee Mains
The number of complex numbers z, satisfying $|z|=1$ and $\left|\frac{z}{\bar{z}}+\frac{\bar{z}}{z}\right|=1$, is
- This topic has 2 replies, 1 voice, and was last updated 2 weeks, 2 days ago by
.
Viewing 3 posts - 1 through 3 (of 3 total)
-
Solution
As $|\mathrm{z}|=\mathrm{r}=1$ so we have $\mathrm{z}=\mathrm{e}^{\mathrm{i} \theta}$ and $\frac{\mathrm{z}}{\overline{\mathrm{z}}}=\mathrm{e}^{\mathrm{i} 2 \theta}$
\[ \left|\frac{\mathrm{z}}{\overline{\mathrm{z}}}+\frac{\overline{\mathrm{z}}}{\mathrm{z}}\right|=\left|\mathrm{e}^{\mathrm{i} 2 \theta}+\mathrm{e}^{-\mathrm{i} 2 \theta}\right|=1 \Rightarrow|\cos 2 \theta|=\frac{1}{2} \]From graph we can conclude that given equation has 8 solution if $\theta \in[0,2 \pi]^{\mathrm{l}}$
Viewing 3 posts - 1 through 3 (of 3 total)
- You must be logged in to reply to this topic.
