Show, as a consequence of De Moivre's Theorem, that all roots of the equation zn =...

 

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Show, as a consequence of De Moivre's Theorem, that all roots of the equation zn = 1 are located on the unit circle, and the roots come in conjugate pairs (except for real roots which are their own conjugates). Finally conclude that the roots form the vertices of a regular polygon with n sides (or n vertices) with one of the vertices located at the complex number 1. Show, as a consequence of De Moivre's Theorem, that all roots of the equation zn = 1 are located on the unit circle, and the roots come in conjugate pairs (except for real roots which are their own conjugates). Finally conclude that the roots form the vertices of a regular polygon with n sides (or n vertices) with one of the vertices located at the complex number 1.