If ω = z − 3 1 i z and ∣ ω ∣ = 1 , then z lies on

As given w = z − 3 1 i z ⇒ ∣ w ∣ = ∣ z − 3 1 i ∣ ∣ z ∣ = 1 ⇒ distance of z from origin and point ( 0 , 3 1 ) is same hence z lies on bisector of the line joining points ( 0 , 0 ) and ( 0 , 1/3 ) . Hence z lies on a straight line.

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Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minPYQ_2005

MathematicsMediumsingle choice

If $ω = \frac{z}{z - \frac{1}{3} i}$ and $∣ ω ∣ = 1$ , then $z$ lies on

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As given $w = \frac{z}{z - \frac{1}{3} i} \Rightarrow ∣ w ∣ = \frac{∣ z ∣}{∣ z - \frac{1}{3} i ∣} = 1 \Rightarrow$ distance of $z$ from origin and point $(0, \frac{1}{3})$ is same hence $z$ lies on bisector of the line joining points $(0, 0)$ and $(0, 1/3)$ . Hence $z$ lies on a straight line.

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2005

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