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If z satisfies abs(z-1)+abs(z+1)=2, then...

If z satisfies `abs(z-1)+abs(z+1)=2`, then locus of z is

A

A straight line passing through z=1 & z=-1

B

Circle

C

A line segment

D

Ellipse

Text Solution

Verified by Experts

The correct Answer is:
1

`abs(z-1) and abs(z+1)` represent distance of complex No. of z from 1 and -1 respectively in the Argand plane Now distance between z=-1 and z=1 is 2 & `abs(z-1)+abs(z+1)`=2 so locus will be line segment joining -1 & 1.
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