The complex number z=z+i y which satisfies the equation |(z-3 i)/(z+3 i)|=1, lies on

Correct answer: A. the X -axis |(z-3 i)/(z+3 i)|=1 |z-3 i|=|z+3 i| [if |z-z_ 1 |=|z+z_ 2 |, then it is a perpendicular bisector of z_ 1 and z_ 2 ] Hence, perpendicular bisector of (0,3) and (0,-3) is X -axis.

BITSAT 2014

Exam: BITSAT
Year: 2014
Subject: Mathematics
Chapter: Complex Number

BITSAT 2014 · Mathematics · Complex Number

The complex number z=z+i y which satisfies the equation |(z-3...

The complex number

z=z+i y

which satisfies the equation

\left|\frac{z-3 i}{z+3 i}\right|=1,

lies on

Options

Athe $X$ -axis
Bthe straight line $y=3$
Ca circle passing through origin
DNone of the above

Correct answer

A. the $X$ -axis

Step-by-step solution

\left|\frac{z-3 i}{z+3 i}\right|=1 \Rightarrow|z-3 i|=|z+3 i|

[if

\left|z-z_{1}\right|=\left|z+z_{2}\right|,

then it is a perpendicular bisector of

z_{1} and z_{2}

] Hence, perpendicular bisector of (0,3) and (0,-3) is

X

-axis.

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