Question:
If $\mathrm{S}=\left\{\mathrm{z} \in \mathbb{C}: \frac{\mathrm{z}-i}{\mathrm{z}+2 i} \in \mathbb{R}\right\}$, then $:$
Correct Option: , 4
Solution:
Given $\frac{\mathrm{z}-\mathrm{i}}{\mathrm{z}+2 \mathrm{i}} \in \mathrm{R}$
Then $\arg \left(\frac{z-i}{z+2 i}\right)$ is 0 or $\Pi$
$\Rightarrow \mathrm{S}$ is straight line in complex
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