JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

Let

a

be a complex number such that

\left| a \right| < 1

and

{z_1},\;{z_2}, \ldots

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 is

View answer and explanation

Correct option: C

\left| {z - \frac{1}{{1 - a}}} \right| = \frac{1}{{\left| {1 - a} \right|}}

Option C (

\left| {z - \frac{1}{{1 - a}}} \right| = \frac{1}{{\left| {1 - a} \right|}}

) is correct because the vertices lie within a circle centered at 1/(1-a) with radius 1/|1-a|.

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