Let z be complex number such that
\(\left|\frac{z-i}{z+2i}\right|=1\)
and \(|z|=\frac{5}{2}\).
Then the value of \(|z+3i|\) is :
\(\left|\frac{z-i}{z+2i}\right|=1\)
and \(|z|=\frac{5}{2}\).
Then the value of \(|z+3i|\) is :
Show Hint
- \(2\sqrt{3}\)
- \(\sqrt{10}\)
- \(\frac{15}{4}\)
- \(\frac{7}{2}\)
The Correct Option is D
Solution and Explanation
\(|z|^2=x^2+\frac14=\frac{25}{4}\Rightarrow x^2=6\).
\(|z+3i|^2=x^2+(y+3)^2=6+\left(\frac52\right)^2=6+\frac{25}{4}=\frac{49}{4}\).
So \(|z+3i|=\frac72\).
Answer: (4) \(\frac{7}{2}\)
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