TS EAMCET · Maths · Complex Number
The equation of the locus of \(z\) such that \(\left|\frac{z-i}{z+i}\right|=2\), where \(z=x+i y\) is a complex number, is
- A \(3 x^2+3 y^2+10 y-3=0\)
- B \(3 x^2+3 y^2+10 y+3=0\)
- C \(3 x^2-3 y^2-10 y-3=0\)
- D \(x^2+y^2-5 y+3=0\)
Answer & Solution
Correct Answer
(B) \(3 x^2+3 y^2+10 y+3=0\)
Step-by-step Solution
Detailed explanation
\(\left|\frac{z-i}{z+i}\right|=2\) \(\because \quad z=x+i y\) \(\therefore \quad\left|\frac{x+i y-i}{x+i y+i}\right|=2\) \(\Rightarrow \quad\left|\frac{x+(y-1) i}{x+(y+1) i}\right|=2\) \(\Rightarrow \quad|x+i(y-1)|=2|x+(y+1) i|\)…
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