diff --git a/src/sage/rings/complex_double.pyx b/src/sage/rings/complex_double.pyx
index bc9018790e4..9deff3dd145 100644
--- a/src/sage/rings/complex_double.pyx
+++ b/src/sage/rings/complex_double.pyx
@@ -97,6 +97,7 @@ import real_mpfr
 RR = real_mpfr.RealField()
 
 from real_double import RealDoubleElement, RDF
+from sage.rings.integer_ring import ZZ
 
 
 from sage.structure.parent_gens import ParentWithGens
@@ -1432,6 +1433,22 @@ cdef class ComplexDoubleElement(FieldElement):
         """
         return True
 
+    def is_integer(self):
+        """
+        Returns True if this number is a integer
+
+        EXAMPLES::
+
+            sage: CDF(0.5).is_integer()
+            False
+            sage: CDF(I).is_integer()
+            False
+            sage: CDF(2).is_integer()
+            True
+        """
+        return (self.real() in ZZ) and (self.imag()==0)
+
+
     def _pow_(self, ComplexDoubleElement a):
         """
         The function returns the complex number `z` raised to the