Let p be a complex number such that |a|<1 and z1,z2,z3,...,zn be the vertices of a polygon such that zk=1+a+a2+a3+...+ak, then the vertices of the polygon lie within the circle.
A
|z−a|=1|1−a|
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B
|z−1|=1|1−a|
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C
∣∣∣z−11−a∣∣∣=1|1−a|
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D
None of these
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Solution
The correct option is B∣∣∣z−11−a∣∣∣=1|1−a| We have, zk=1+a+a2+...+ak=1−ak+11−a