question_answer

Let a be a complex number such that |a| < 1 and \[{{z}_{1}},\,{{z}_{2}}.....\] be vertices of a polygon such that \[{{z}_{k}}=1+a+{{a}^{2}}+.........+{{a}^{k-1}}\].Then the vertices of the polygon lie within a circle

A)  \[|z-a|\,\,=a\]              

B)  \[\left| z-\frac{1}{1-a} \right|=\,|1-a|\]

C)  \[\left| z-\frac{1}{1-a} \right|=\frac{1}{|1-a|}\]

D)  \[|z-(1-a)|\,=\,|1-a|\]

E)  None of these