Complex Numbers 5 Question 14

15.

The value of the expression

$1(2-\omega)\left(2-\omega^{2}\right)+2(3-\omega)\left(3-\omega^{2}\right)+\ldots$

$+(n-1) \cdot(n-\omega)\left(n-\omega^{2}\right)$,

where, $\omega$ is an imaginary cube root of unity, is….

(1996, 2M)

Show Answer

Answer:

Correct Answer: 15. $\frac{n(n+1)}{2}{ }^{2}-n$

Solution:

  1. Here, $\left.T _r=(r-1)(r-\omega)(r-\omega)^{2}\right]=\left(r^{3}-1\right)$

$ \therefore \quad S _n=\sum _{r=1}^{n}\left(r^{3}-1\right)=\frac{n(n+1)}{2}^{2}-n $



NCERT Chapter Video Solution

Dual Pane