The complex number z = z + i y which satisfies the equation z + 3 i z − 3 i = 1 , lies on

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MathematicsComplex NumberGeometric ApplicationMedium2 minPYQ_2014

MathematicsMediumsingle choice

The complex number $z = z + i y$ which satisfies the equation $\frac{z - 3 i}{z + 3 i} = 1,$ lies on

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Solution:

$\frac{z - 3 i}{z + 3 i} = 1 \Rightarrow ∣ z - 3 i ∣ = ∣ z + 3 i ∣$ [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.

Stream:BITSATSubject:MathematicsTopic:Complex NumberSubtopic:Geometric Application

⏱ 2mℹ️ Source: PYQ_2014

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