A) Concyclic
B) Vertices of a parallelogram
C) Vertices of a rhombus
D) In a straight line
Correct Answer: A
Solution :
We have \[|z-{{z}_{1}}|\,=\,|z-{{z}_{2}}|\,=\,|z-{{z}_{3}}|\,=\,|z-{{z}_{4}}|\] Therefore the point having affix \[z\] is equidistant from the four points having affixes \[{{z}_{1}},{{z}_{2}},{{z}_{3}},{{z}_{4}}\]. Thus \[z\] is the affix of either the centre of a circle or the point of intersection of diagonals of a square or rectangle. Therefore \[{{z}_{1}},{{z}_{2}},{{z}_{3}},{{z}_{4}}\] are either concyclic or vertices of a square. Hence \[{{z}_{1}},{{z}_{2}},{{z}_{3}},{{z}_{4}}\] are concyclic.
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