1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider, f ( z )= z 12+2 ⋅ z 11+3 ⋅ z 10+ ldots . .+12 ⋅ z +13 and α= cos (2 π/13)+ i sin (2 π/13), where i =√-1. The value of ( f (α) ⋅ f (α2) ldots f (α12)) is equal to

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

Complex Numbers and Quadratic Equations

Solution:

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