In view of periodicity of trigonometric functions sine and cosine, a complex number can be rewritten in the polar form as follows:

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The  nth roots of  z are determined by expression

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By substituting  m = 0, 1, 2, 3, ...  we obtain all roots  tm  of a complex number. There exist  n  different roots exactly:

The next value of integer  m  gives the root  tn+1  that coincides with  t1:

Note that all roots have the same modulus  , that is, they lie on the circle with the radius  .

There is a simple way to plot all  n  roots of a number  z  when one of the roots is known. We need only to divide the circle with radius    into  n equal parts, starting from the point on the circle that corresponds to a root of  z.

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