# Simplifying complex-valued entries in a matrix

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?

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

• so FullySimplify work for Matrix too? thanks – henry Feb 1 '19 at 1:26
• It threads over lists, yes. – Chip Hurst Feb 1 '19 at 1:27
• I tried it.. and its work.. thanks. – henry Feb 1 '19 at 1:28
      Simplify[ComplexExpand[(-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9)]]
(*  0  *)