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Question
If a complex number z satisfies the following relation |z - 1| + |z + 1| = 2, then the point z lies on
If a complex number z satisfies the following relation |z - 1| + |z + 1| = 2, then the point z lies on
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Solution
The correct option is C line segment
|z - 1| is the distance of z from (1, 0) and |z + 1| is the distance from (-1, 0). Lets consider a point P which is not on the line segment joining A(-1, 0) and B(1, 0). AB = 2 units clearly PA + PB > 2(Triangle inequality).
i.e. If we take any point + z, outside the line segment, |z - 1| + |z + 1| will be more than one.
Also, for any point on the line segment AB, |z - 1| + |z + 1| = 2.
line segment
|z - 1| is the distance of z from (1, 0) and |z + 1| is the distance from (-1, 0). Lets consider a point P which is not on the line segment joining A(-1, 0) and B(1, 0). AB = 2 units clearly PA + PB > 2(Triangle inequality).
i.e. If we take any point + z, outside the line segment, |z - 1| + |z + 1| will be more than one.
Also, for any point on the line segment AB, |z - 1| + |z + 1| = 2.
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