WBJEE · Maths · Complex Number
The complex number \(z\) satisfying the equation \(|z-i|=|z+1|=1\) is
- A 0
- B \(1+i\)
- C \(-1+i\)
- D \(1-i\)
Answer & Solution
Correct Answer
(C) \(-1+i\)
Step-by-step Solution
Detailed explanation
We have, \(|z-i|=|z+1|=1\) Let, \(\quad z=x+iy\) \(\therefore \quad|z-i|=1\) \(\Rightarrow \quad|x+iy-i \mid=1\) \(\Rightarrow|x+(y-1) i|=1\) \(\Rightarrow \quad x^{2}+(y-1)^{2}=1\) Also, \(\quad|z+1|=1\) \(\Rightarrow \quad|x+ iy+1 \mid=1\) \(\Rightarrow \quad|(x+1)+i y|=1\)…
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