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Complex Root


sqrt( ): (N x C') -> C'
sqrtn(z) := <sqrtn(z0), z1/n>.

Proposition: For every n in N>0 and z in C', the n-th roots of z are sqrt^n(z) and the n-1 values that have the same distance from the origin and their angle shifted by multiples of 2 pi /n:

forall n in N>0, z in C':
   let r = sqrtn(z):
   (forall s in C': z = sn <=> exists i in N: s = <r0, shift(r1+2 pi i/n)>).

Author: Wolfgang Schreiner
Last Modification: December 7, 1999

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