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Jul 28th, 2016
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  1. In[1] := FullSimplify[(x - I y)^n (x + I y)^n,
  2. Assumptions -> {x [Element] Reals, y [Element] Reals, 0 < n}]
  3. Out[1] := (x - I y)^n (x + I y)^n
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