Let (where is natural number which exclusively lies between 8 and 24) are the…

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Number and Algebra · Number and Algebra

Problem

Let

Z_r, r = 1, 2, 3, \dots, n

(where

n

is natural number which exclusively lies between 8 and 24) are the

n

distinct roots of equation

nC_1 x + nC_2 x^2 + nC_3 x^3 + \dots + nC_n x^n = 0

in argand plane. If there exist exactly one

Z_r

r \in \{1, 2, 3, \dots, n\}

such that

\arg\left(\frac{(Z_r - (-1 + \sqrt{2}i))}{(-1) - (-1 + \sqrt{2}i)}\right)

= \frac{\pi}{4}

, then sum of all possible values of 'n' is equal to: