TS EAMCET · Maths · Complex Number
The locus of the point \(z=x+i y\) satisfying the equation \(\left|\frac{z-1}{z+1}\right|=1\) is given by :
- A \(x=0\)
- B \(y=0\)
- C \(x=y\)
- D \(x+y=0\)
Answer & Solution
Correct Answer
(A) \(x=0\)
Step-by-step Solution
Detailed explanation
\(\because \quad\left|\frac{z-1}{z+1}\right|=1\) \(\Rightarrow \quad\left|\frac{x+i y-1}{x+i y+1}\right|=1\) \(\Rightarrow \quad|(x-1)+i y|=|(x+1)+i y|\) \(\Rightarrow \quad \sqrt{(x-1)^2+y^2}=\sqrt{(x+1)^2+y^2}\) \(\Rightarrow \quad x^2-2 x+1+y^2=x^2+1+2 x+y^2\)…
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