JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(\mathrm{S}=\left\{\mathrm{z} \in \mathbb{C}: \frac{\mathrm{z}-i}{\mathrm{z}+2 i} \in \mathbb{R}\right\}\), then :
- A \(S\) contains exactly two elements
- B \(S\) contains only one element
- C \(\mathrm{S}\) is a circle in the complex plane
- D \(\mathrm{S}\) is a straight line in the complex plane
Answer & Solution
Correct Answer
(D) \(\mathrm{S}\) is a straight line in the complex plane
Step-by-step Solution
Detailed explanation
Given \(\frac{\mathrm{z}-\mathrm{i}}{\mathrm{z}+2 \mathrm{i}} \in \mathrm{R}\) Then \(\arg \left(\frac{\mathrm{z}-\mathrm{i}}{\mathrm{z}+2 \mathrm{i}}\right)\) is \(0\) or \(\Pi\) \(\Rightarrow \mathrm{S}\) is straight line in complex
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