Assuming[ci != 0, Sign[ci]^2==1]

Questions
1

May be I am wrong, but I thing that correct result should be True.

Am I making a mistake, or not?

In[2]:=  Assuming[ci != 0, (Sign[ci]^2 == 1) // FullSimplify]

Out[2]= Sign[ci]^2 == 1

Thanks!

2

Mathematica thinks with complex numbers and the identity is not true with complex numbers.

Assuming[ci != 0 && Element[ci, Reals], (Sign[ci]^2 == 1) // 
  FullSimplify]
3

Thank you, Sean.

It was my mistake, I tried Assuming[ci >0 and also Assuming[ci <0 and I didn’t noticed, that this implicitly means, that ci is real, but ci != 0 doesnt mean, that ci should be real.

Assuming[{ci != 0 && ci \[Element] Reals}, Sign[ci]^2 == 1 // FullSimplify]

works as expected.