If $w = \frac{z}{{z - \frac{1}{3}i}}$ and $\left| w \right| = 1$, then $z$ lies on

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

w = \frac{z}{{z - \frac{1}{3}i}}

and

\left| w \right| = 1

, then

z

lies on

View answer and explanation

Correct option: B

A straight line

A straight line. Option B is correct because the condition |w| = 1 leads to a linear equation in terms of the real and imaginary parts of z.

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