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This question already has an answer here:

Finding all roots, and I know there are four f them, of this (1 - i)^(1/4) Not only real, but imaginary as well

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marked as duplicate by Yves Klett, Artes, Öskå, ubpdqn, ybeltukov Oct 21 '14 at 12:55

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  • $\begingroup$ The duplicate here indeed is not really what your question is about. The answer by Mark should help you though (my motivation to close was that the solution can be found in the documentation). $\endgroup$ – Yves Klett Oct 22 '14 at 11:03
  • $\begingroup$ It did help me a lot. Thank you very much! $\endgroup$ – Sausan Oct 22 '14 at 11:13
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You mean like this?

Reduce[x^4 == 1 - I, x] // N
x==-1.06955+0.212748 I||x==-0.212748-1.06955 I||x==0.212748+1.06955 I||x==1.06955-0.212748 I
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  • $\begingroup$ Can also just use Solve[x^4 == 1 - I, x] $\endgroup$ – Nasser Oct 21 '14 at 4:29
  • $\begingroup$ In this case, yes. Though Reduce promises a complete set of results equivalent to the original expression, whereas Solve has caveats, such as: "Solve uses non-equivalent transformations to find solutions of transcendental equations and hence it may not find some solutions and may not establish exact conditions on the validity of the solutions found." $\endgroup$ – Mark Adler Oct 21 '14 at 4:56

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