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I have a matrix where some entries are complex or roots of unity. For example, 

(-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9)

is one such entry and it is equal to 0.

When I send such an entry to Wolfram|Alpha, it gives me zero. But I have matrix full of such identities, so I want to do the simplification on the whole matrix and inside Mathematica.

Is there is anyway I can do that?

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2 Answers 2

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Here's a few approaches:

FullSimplify[(-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9)]

0

Simplify[ExpToTrig[(-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9)]]

0

PossibleZeroQ[(-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9)]

True
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3
  • $\begingroup$ so FullySimplify work for Matrix too? thanks $\endgroup$
    – henry
    Feb 1, 2019 at 1:26
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    $\begingroup$ It threads over lists, yes. $\endgroup$
    – Greg Hurst
    Feb 1, 2019 at 1:27
  • $\begingroup$ I tried it.. and its work.. thanks. $\endgroup$
    – henry
    Feb 1, 2019 at 1:28
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      Simplify[ComplexExpand[(-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9)]]
 (*  0  *)
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