Q. Consider, $f (z) = z^{12} + 2 \cdot z^{11} + 3 \cdot z^{10} + \dots .. + 12 \cdot z + 13$ and $α = cos \frac{2 π}{13} + i sin \frac{2 π}{13}$ , where $i = - 1$ .
The value of $(f (α) \cdot f (α^{2}) \dots f (α^{12}))$ is equal to

38 112 Complex Numbers and Quadratic Equations Report Error

A

$(13)^{11}$

B

$(13)^{12}$

C

$(13)^{13}$

D

$(13)^{14}$

Solution:

Correct answer is (a) $(13)^{11}$