diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 5d2f2ca2216..cc318f93e53 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -117,8 +117,8 @@
     1
     sage: QQbar((-8)^(1/3))
     1.000000000000000? + 1.732050807568878?*I
-    sage: AA((-8)^(1/3))
-    -2
+    sage: AA(8^(1/3))
+    2
     sage: QQbar((-4)^(1/4))
     1 + 1*I
     sage: AA((-4)^(1/4))
@@ -298,8 +298,8 @@
     sage: n = (rt2 + rt3)^5; n
     308.3018001722975?
     sage: sage_input(n)
-    R.<x> = AA[]
-    v1 = AA.polynomial_root(AA.common_polynomial(x^2 - 2), RIF(RR(1.4142135623730949), RR(1.4142135623730951))) + AA.polynomial_root(AA.common_polynomial(x^2 - 3), RIF(RR(1.7320508075688772), RR(1.7320508075688774)))
+    R.<x> = QQbar[]
+    v1 = QQbar.polynomial_root(AA.common_polynomial(x^2 - 2), CIF(RIF(RR(1.4142135623730949), RR(1.4142135623730951)), RIF(RR(0)))).real() + QQbar.polynomial_root(AA.common_polynomial(x^2 - 3), CIF(RIF(RR(1.7320508075688772), RR(1.7320508075688774)), RIF(RR(0)))).real()
     v2 = v1*v1
     v2*v2*v1
 
@@ -335,8 +335,8 @@
     sage: n = rt2^2
     sage: sage_input(n, verify=True)
     # Verified
-    R.<x> = AA[]
-    v = AA.polynomial_root(AA.common_polynomial(x^2 - 2), RIF(RR(1.4142135623730949), RR(1.4142135623730951)))
+    R.<x> = QQbar[]
+    v = QQbar.polynomial_root(AA.common_polynomial(x^2 - 2), CIF(RIF(RR(1.4142135623730949), RR(1.4142135623730951)), RIF(RR(0)))).real()
     v*v
     sage: sage_input(n, verify=True)
     # Verified
diff --git a/src/sage/symbolic/expression_conversion_algebraic.py b/src/sage/symbolic/expression_conversion_algebraic.py
index 924ab876115..93d33f380ca 100644
--- a/src/sage/symbolic/expression_conversion_algebraic.py
+++ b/src/sage/symbolic/expression_conversion_algebraic.py
@@ -101,6 +101,12 @@ def arithmetic(self, ex, operator):
             sage: L = QuadraticField(3, embedding=-AA(3).sqrt())
             sage: bool(L.gen() == -sqrt(3))
             True
+
+        Test that :issue:12745 is fixed:
+
+            sage: x = exp(2*I*pi/7) + exp(-2*I*pi/7)
+            sage: AA(x)
+            1.246979603717467?
         """
         # We try to avoid simplifying, because maxima's simplify command
         # can change the value of a radical expression (by changing which
@@ -121,14 +127,6 @@ def arithmetic(self, ex, operator):
         except TypeError:
             pass
 
-        if operator is pow:
-            from sage.symbolic.constants import e, pi, I
-            from sage.rings.rational_field import QQ
-
-            base, expt = ex.operands()
-            if base == e and expt / (pi * I) in QQ:
-                return exp(expt)._algebraic_(self.field)
-
         raise TypeError("unable to convert %r to %s" % (ex, self.field))
 
     def composition(self, ex, operator):