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De Moivre’s Theorem

Raising numbers to powers as well as extracting their roots are fundamental operations in the set of complex numbers. De Moivre's theorem provides us with a general method for these operations. Here is the theorem:

If z = r [(cos a) + i (sin a)] is a complex number in polar form

then for a positive integer n, zn = rn [(cos na) + i (sin na)]