Repository: sympy/sympy

Issue:
conjugate of real expression should not change expression
The square root of a real quantity does not seem to be detected as real. The last two expressions are not evaluated as 0.
```
x, y = symbols("x, y", real=True)
r = sqrt(x**2+y**2)
simplify(conjugate(r)-r)
simplify(conjugate(re(r))-r)
```

Discussion:

Patch:
diff --git a/sympy/core/power.py b/sympy/core/power.py
index ac07ca460f..5e523e689e 100644
--- a/sympy/core/power.py
+++ b/sympy/core/power.py
@@ -675,6 +675,8 @@ def _eval_conjugate(self):
             expanded = expand_complex(self)
             if expanded != self:
                 return c(expanded)
+        if self.is_real:
+            return self
 
     def _eval_transpose(self):
         from sympy.functions.elementary.complexes import transpose


Test patch:
diff --git a/sympy/core/tests/test_complex.py b/sympy/core/tests/test_complex.py
index 005cecb9c9..85fd305bbb 100644
--- a/sympy/core/tests/test_complex.py
+++ b/sympy/core/tests/test_complex.py
@@ -210,3 +210,11 @@ def test_issue_5429():
 def test_issue_4124():
     from sympy import oo
     assert expand_complex(I*oo) == oo*I
+
+def test_issue_11518():
+    x = Symbol("x", real=True)
+    y = Symbol("y", real=True)
+    r = sqrt(x**2 + y**2)
+    assert conjugate(r) == r
+    s = abs(x + I * y)
+    assert conjugate(s) == r