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प्रश्न
The equation |z + 1 – i| = |z – 1 + i| represents a ______.
विकल्प
Straight line
Circle
Parabola
Hyperbola
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उत्तर
The equation |z + 1 – i| = |z – 1 + i| represents a straight line.
Explanation:
|z + 1 – i| = |z – 1 + i|
⇒ |z – (–1 + i)| = |z – (1 – i)|
⇒ PA = PB Where A denotes the point (–1, 1), B denotes the point (1, –1) and P denotes the point (x, y).
⇒ z lies on the perpendicular bisector of the line joining A and B and perpendicular bisector is a straight line.
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