Question

If ‘z’ is complex number then the locus of ‘z’ satisfying the condition |2z – 1| = |z – 1| is

• A. Perpendicular bisector of line segment joining $\frac{1}{2}$and 1
• B. Circle
• C. Parabola
• D. None of the above curves

Answer 1

Answer: (B)

Circle

Answer 2

Sol. 2$\left| z - \frac{1}{2} \right|$ = |z – 1| \ $\frac{|z - 1|}{|z - 1/2|}$= 2

So locus of z is a circle