[JEE Advanced 1984] if 1 a 1 a 2 a n 1 are the n roots of
If $1,a_1,a_2,\dots,a_{n-1}$ are the $n$ roots of unity, show that $(1-a_1)(1-a_2)\cdots(1-a_{n-1})=n$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Answer: Proved $=n$.
$x^n-1=\prod_{k}(x-a_k)$, so $\frac{x^n-1}{x-1}=1+x+\cdots+x^{n-1}=\prod_{k=1}^{n-1}(x-a_k)$. Putting $x=1$ gives $\prod(1-a_k)=n$.
JEE Advanced 1984 · Complex Numbers — verified solution by the Vidaara Team.
Log in to post your own answer or join the discussion.
No comments yet — start the discussion.