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12 Questions around this concept.
The roots of the equation
If
We solve the nth root of unity the same as the cube root, only the value becomes n instead of 3 .
Let
Using the De-moivre theorem, it can be written as
Now for
Let,
Then, nth root of unity are
l.e.
So these roots of unity are in geometric progression with a common ratio
(We will study geometric progression and common ratio in the chapter Sequences and Series later)
The sum of nth roots of unity
As all these numbers are roots of the polynomial equation
So, using the sum of roots relation, we can see that the sum of roots
Product of nth roots of unity
As all these numbers are roots of the polynomial equation
So, using the product of roots relation, we can see that the product of roots will be 1 if
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