WBJEE · Maths · Complex Number
If \(|z+i|-|z-1|=|z|-2=0\) for a complex number \(z\), then \(z=\)
- A \(\sqrt{2}(1+i)\)
- B \(\sqrt{2}(1-i)\)
- C \(\sqrt{2}(-1+i)\)
- D \(\sqrt{2}(-1-\mathrm{i})\)
Answer & Solution
Correct Answer
(C) \(\sqrt{2}(-1+i)\)
Step-by-step Solution
Detailed explanation
\(|z| =2\) represents circle \(|z+i|=|z-1|\) represents Solving \(x^{2}+y^{2}=4\) and \(y=-x\) \(z=\sqrt{2}(1-i), \quad \sqrt{2}(-1+i)\)
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