diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index f318bfd5d..096438f96 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -399,8 +399,16 @@ template<typename Derived> class MatrixBase
 
 /////////// Geometry module ///////////
 
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /// \internal helper struct to form the return type of the cross product
+    template<typename OtherDerived> struct cross_product_return_type {
+      typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
+      typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> type;
+    };
+    #endif // EIGEN_PARSED_BY_DOXYGEN
     template<typename OtherDerived>
-    PlainObject cross(const MatrixBase<OtherDerived>& other) const;
+    typename cross_product_return_type<OtherDerived>::type
+    cross(const MatrixBase<OtherDerived>& other) const;
     template<typename OtherDerived>
     PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
     PlainObject unitOrthogonal(void) const;
diff --git a/Eigen/src/Geometry/OrthoMethods.h b/Eigen/src/Geometry/OrthoMethods.h
index 64ca52e16..52b469881 100644
--- a/Eigen/src/Geometry/OrthoMethods.h
+++ b/Eigen/src/Geometry/OrthoMethods.h
@@ -35,7 +35,7 @@
   */
 template<typename Derived>
 template<typename OtherDerived>
-inline typename MatrixBase<Derived>::PlainObject
+inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
 MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
 {
   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
@@ -45,10 +45,10 @@ MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
   // optimize such a small temporary very well (even within a complex expression)
   const typename internal::nested<Derived,2>::type lhs(derived());
   const typename internal::nested<OtherDerived,2>::type rhs(other.derived());
-  return typename internal::plain_matrix_type<Derived>::type(
-    lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1),
-    lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2),
-    lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)
+  return typename cross_product_return_type<OtherDerived>::type(
+    internal::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+    internal::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+    internal::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
   );
 }
 
@@ -62,9 +62,9 @@ struct cross3_impl {
   run(const VectorLhs& lhs, const VectorRhs& rhs)
   {
     return typename internal::plain_matrix_type<VectorLhs>::type(
-      lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1),
-      lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2),
-      lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0),
+      internal::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+      internal::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+      internal::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
       0
     );
   }
@@ -121,16 +121,16 @@ VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& ot
   if(Direction==Vertical)
   {
     eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
-    res.row(0) = _expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1);
-    res.row(1) = _expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2);
-    res.row(2) = _expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0);
+    res.row(0) = (_expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1)).conjugate();
+    res.row(1) = (_expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2)).conjugate();
+    res.row(2) = (_expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0)).conjugate();
   }
   else
   {
     eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
-    res.col(0) = _expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1);
-    res.col(1) = _expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2);
-    res.col(2) = _expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0);
+    res.col(0) = (_expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1)).conjugate();
+    res.col(1) = (_expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2)).conjugate();
+    res.col(2) = (_expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0)).conjugate();
   }
   return res;
 }
diff --git a/test/geo_orthomethods.cpp b/test/geo_orthomethods.cpp
index 9152d99c8..020ae7103 100644
--- a/test/geo_orthomethods.cpp
+++ b/test/geo_orthomethods.cpp
@@ -33,6 +33,7 @@
 
 template<typename Scalar> void orthomethods_3()
 {
+  typedef typename NumTraits<Scalar>::Real RealScalar;
   typedef Matrix<Scalar,3,3> Matrix3;
   typedef Matrix<Scalar,3,1> Vector3;
 
@@ -44,6 +45,9 @@ template<typename Scalar> void orthomethods_3()
 
   // cross product
   VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
+  VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));
+  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));
+  VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));
   Matrix3 mat3;
   mat3 << v0.normalized(),
          (v0.cross(v1)).normalized(),
@@ -68,6 +72,12 @@ template<typename Scalar> void orthomethods_3()
   v40.w() = v41.w() = v42.w() = 0;
   v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());
   VERIFY_IS_APPROX(v40.cross3(v41), v42);
+  
+  // check mixed product
+  typedef Matrix<RealScalar, 3, 1> RealVector3;
+  RealVector3 rv1 = RealVector3::Random();
+  VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1));
+  VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1));
 }
 
 template<typename Scalar, int Size> void orthomethods(int size=Size)
@@ -115,6 +125,7 @@ void test_geo_orthomethods()
   for(int i = 0; i < g_repeat; i++) {
     CALL_SUBTEST_1( orthomethods_3<float>() );
     CALL_SUBTEST_2( orthomethods_3<double>() );
+    CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() );
     CALL_SUBTEST_1( (orthomethods<float,2>()) );
     CALL_SUBTEST_2( (orthomethods<double,2>()) );
     CALL_SUBTEST_1( (orthomethods<float,3>()) );