Ans: A.
How?

Number of values of z (real or complex) simultaneously satisfying the system of equations 1 + z + z 2 + z 3 +..........+ z 17 = 0 and 1 + z + z 2 + z 3 + ...........+z 13 = 0 is
(A) 1
(B) 2
(C) 3
(D) 4

Dear Student,

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​​​​​​Therefore, we see that z=-1 is the only value which satisfies both the equations.

So, Total number of values satisfying both the equation = 1
​​​​​​So, Option A is the correct answer

Regards

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