JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z\) be complex number such that \(\left|\frac{z-i}{z+2 i}\right|=1\) and \(|z|=\frac{5}{2} \cdot\) Then the value of \(|z+3 i|\) is
- A \(\sqrt{10}\)
- B \(2 \sqrt{3}\)
- C \(\frac{7}{2}\)
- D \(\frac{15}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{2}\)
Step-by-step Solution
Detailed explanation
\(\left|\frac{z-i}{z+2 i}\right|=1\) \(\Rightarrow|z-i|=|z+2 i|\) \(\Rightarrow \quad z\) lies on perpendicular bisector of \((0,1)\) and \((0,-2)\) \(\Rightarrow \quad \operatorname{Im} z=-\frac{1}{2}\) Let \(z=x-\frac{i}{2}\)…
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