# sympy__sympy-17139
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on the architect's analysis and the traceback, I can generate the patch. The issue is at line 504 in the `_f` function inside `_TR56`. The comparison `rv.exp < 0` fails for complex exponents like `I`.

The fix should change from using `<` comparison (which raises TypeError for complex numbers) to using the `is_negative` property, which safely returns `None` for complex numbers.

--- a/sympy/simplify/fu.py
+++ b/sympy/simplify/fu.py
@@ -501,7 +501,7 @@ def _TR56(rv, f, g, h, max, pow):
     def _f(rv):
         # I'm not sure if this transformation should target all even powers
         # or only those expressible as powers of 2. Also, should it only
-        # make the changes in powers that appear in sums -- makingass'am am2am A um.g-level changes
+        # make the changes in powers that appear in sums -- making
         # doesn't seem to help according to tests.
         if not (rv.is_Pow and rv.base.func == f):
             return rv
@@ -501,10 +501,10 @@ def _TR56(rv, f, g, h, max, pow):
         if not (rv.is_Pow and rv.base.func == f):
             return rv

-        if (rv.exp < 0) == True:
+        if rv.exp.is_negative:
             return rv
-        if (rv.exp > max) == True:
+        if rv.exp.is_number and rv.exp.is_real and (rv.exp > max) == True:
             return rv
         if rv.exp == 2:
             return h(g(rv.base.args[0])**2)

Let me provide a cleaner patch based on the standard sympy pattern:

--- a/sympy/simplify/fu.py
+++ b/sympy/simplify/fu.py
@@ -501,9 +501,9 @@ def _TR56(rv, f, g, h, max, pow):
         if not (rv.is_Pow and rv.base.func == f):
             return rv
 
-        if (rv.exp < 0) == True:
+        if rv.exp.is_negative:
             return rv
-        if (rv.exp > max) == True:
+        if rv.exp.is_real and (rv.exp > max) == True:
             return rv
         if rv.exp == 2:
             return h(g(rv.base.args[0])**2)