Question

If Z_r : r = 1, 2, 3,….., 50 are the roots of the equation $\sum_{r = 0}^{50}{(Z)^{r}}$= 0, then the value of $\sum_{r = 1}^{50}\frac{1}{Z_{r} - 1}$ is :

• A. –85
• B. –25
• C. 25
• D. 75

Answer 1

Answer: (B)

–25

Answer 2

Sol. Z^r =$e^{i\frac{2\pi r}{50}}$= Z_r

$\sum_{r = 1}^{50}\frac{1}{Z_{r - 1}}$= –25