JEE MAIN - Mathematics (2021 - 27th August Morning Shift - No. 4)
If $$S = \left\{ {z \in C:{{z - i} \over {z + 2i}} \in R} \right\}$$, then :
S contains exactly two elements
S contains only one element
S is a circle in the complex plane
S is a straight line in the complex plane
Explanation
Given $${{z - i} \over {z + 2i}} \in R$$
Then $$\arg \left( {{{z - i} \over {z + 2i}}} \right)$$ is 0 or $$\pi $$
_27th_August_Morning_Shift_en_4_1.png)
$$\Rightarrow$$ S is straight line in complex
Then $$\arg \left( {{{z - i} \over {z + 2i}}} \right)$$ is 0 or $$\pi $$
$$\Rightarrow$$ S is straight line in complex
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