Question:
The complex number \(z=z+iy\) which satisfies the equation
\[
\left|\frac{z-3i}{z+3i}\right|=1
\]
lies on:
The complex number \(z=z+iy\) which satisfies the equation
\[
\left|\frac{z-3i}{z+3i}\right|=1
\]
lies on:
Show Hint
\(|z-a|=|z-b|\) represents perpendicular bisector of line joining \(a\) and \(b\).
Updated On: Mar 24, 2026
- the X-axis
- the straight line \(y=3\)
- a circle passing through origin
- None of the above
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The Correct Option is A
Solution and Explanation
Step 1: Given \(|z-3i|=|z+3i|\).
Step 2: This represents locus of points equidistant from \(3i\) and \(-3i\).
Step 3: The perpendicular bisector is the X-axis.
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