JEE Mains · Maths · STD 11 - 4.1 complex nubers
The equation \(\arg \left(\frac{\mathrm{z}-1}{\mathrm{z}+1}\right)=\frac{\pi}{4}\) represents a circle with:
- A centre at \((0,-1)\) and radius \(\sqrt{2}\)
- B centre at \((0,1)\) and radius \(\sqrt{2}\)
- C centre at \((0,0)\) and radius \(\sqrt{2}\)
- D centre at \((0,1)\) and radius \(2\)
Answer & Solution
Correct Answer
(B) centre at \((0,1)\) and radius \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
In \(\triangle \mathrm{OAC}\) \(\sin \left(\frac{\pi}{4}\right)=\frac{1}{\mathrm{AC}}\) \(\Rightarrow \mathrm{AC}=\sqrt{2}\) Also, \(\tan \frac{\pi}{4}=\frac{\mathrm{OA}}{\mathrm{OC}}=\frac{1}{\mathrm{OC}}\) \(\Rightarrow \mathrm{OC}=1\) \(\therefore\) centre \((0,1) ;\) Radius…
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