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  4. If S = z ∈ C: ( Z -i/ z +2 i) ∈ R then :

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Q. If $S =\left\{ z \in C : \frac{ Z -i}{ z +2 i} \in R \right\}$, then :

JEE MainJEE Main 2021Complex Numbers and Quadratic Equations

Solution:

Given $\frac{ z - i }{ z +2 i } \in R$
Then $\arg \left(\frac{ z - i }{ z +2 i }\right)$ is $0$ or $\Pi$
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$\Rightarrow S$ is straight line in complex