Roots of Unity

Given a small integer n, print all the n'th roots of unity up to 6 significant digits. We basically need to find all roots of equation xⁿ - 1.

Examples: 

Input : n = 1
Output : 1.000000 + i 0.000000
x - 1 = 0 , has only one root i.e., 1

Input : 2
Output : 1.000000 + i 0.000000
 -1.000000 + i 0.000000
x2 - 1 = 0 has 2 distinct roots, i.e., 1 and -1 

Any complex number is said to be root of unity if it gives 1 when raised to some power. 
nth root of unity is any complex number such that it gives 1 when raised to the power n.  

Mathematically, 
An nth root of unity, where n is a positive integer 
(i.e. n = 1, 2, 3, …) is a number z satisfying the
equation 

z^n = 1
or , 
z^n - 1 = 0

We can use the De Moivre's formula here ,  

( Cos x + i Sin x )^k = Cos kx + i Sin kx

Setting x = 2*pi/n, we can obtain all the nth roots 
of unity, using the fact that Nth roots are set of 
numbers given by,

Cos (2*pi*k/n) + i Sin(2*pi*k/n)
Where, 0 <= k < n

Using the above fact we can easily print all the nth roots of unity ! 

Below is the program for the same. 

Output: 

1.000000 + i 0.000000
1.000000 + i 0.000000
-1.000000 + i 0.000000
1.000000 + i 0.000000
-0.500000 + i 0.866025
-0.500000 - i 0.866025

References: Wikipedia