NSolve with conditions on complex solutions

I’m trying to solve a system of coupled equations where the results are expected to be complex. The problem is that I want only the solutions that fall in range [-i,i], when I put this condition, I got error about invalid comparison of complexes. Is there any way to put this condition on the obtained solutions.

question ver1.nb (33.9 KB)

What do you mean by “range [-i,i]”? Is that the segment between the points -i and i in the complex plane? Then the conditions should be Re[variable]==0&&-1<=Im[variable]<=1.

I meant the real and imaginary parts should be ranged between -1 and 1

I tried to define the conditions as
-1<Re[]<1 , -1<Im[]<1 but I got this error
NSolve::precbd: Requested precision [DoubleStruckCapitalC] is not a machine-sized real number between $MinPrecision and $MaxPrecision.

The problem is solved.
Thanks for your help