Nth roots of unity

Let oin— 1, where n is a positive integer. The roots of this equation are the nth roots of unity. The number 1 has absolute value 1 and its phase can... 

The complex number z is a primitive nth root of unity if zn=l but zk is not equal to 1 for any positive integer k less than n. probability... 

De Moivre s theorem can be used to determine the nth roots of unity, namely the n complex roots of the equation... 

This last equation means that xc must be an nth root of unity such numbers, which are in general complex, lie on the unit circle in the complex plane and have the form e . Then, by (4),... 

The characters of the one-dimonsional species must satisfy the same multiplication rules as the group operations. In particular, this observation immediately limits the possible characters of C2 to 1. In the case of the cyclic groups, C , it was found that xc was an nth root of unity, d his must likewise be true in the dihedral groups, but sincMJ C and belong to the same class. 

Does the set of the nth roots of unity [Eq. (1.36)] with the rule of combination being ordinary multiplication form a group Justify your answer. 

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