diff --git a/lib/Dialect/mhlo/transforms/lower_complex_patterns.td b/lib/Dialect/mhlo/transforms/lower_complex_patterns.td
index d132297..f67c786 100644
--- a/lib/Dialect/mhlo/transforms/lower_complex_patterns.td
+++ b/lib/Dialect/mhlo/transforms/lower_complex_patterns.td
@@ -87,3 +87,11 @@ def : Pat<(HLO_ExpOp HLO_ComplexTensor:$val),
             (HLO_CosOp (HLO_ImagOp:$imag $val)),
             (HLO_ExpOp:$exp (HLO_RealOp:$real $val))),
            (HLO_MulOp (HLO_SinOp $imag), $exp))>;
+
+foreach pair = [[HLO_COMPARISON_DIRECTION_NE, HLO_OrOp],
+                [HLO_COMPARISON_DIRECTION_EQ, HLO_AndOp]] in {
+  def : Pat<(HLO_CompareOp HLO_ComplexTensor:$lhs, HLO_ComplexTensor:$rhs, pair[0], $compare_type),
+            (pair[1]
+             (HLO_CompareOp (HLO_RealOp $lhs), (HLO_RealOp $rhs), pair[0], $compare_type),
+             (HLO_CompareOp (HLO_ImagOp $lhs), (HLO_ImagOp $rhs), pair[0], $compare_type))>;
+}
diff --git a/tests/lower-complex.mlir b/tests/lower-complex.mlir
index 141c238..ed9e997 100644
--- a/tests/lower-complex.mlir
+++ b/tests/lower-complex.mlir
@@ -238,3 +238,35 @@ func @exp_unranked(%arg0 : tensor<*xcomplex<f32>>) -> (tensor<*xcomplex<f32>>) {
   // CHECK: [[OUT]]
   return %0 : tensor<*xcomplex<f32>>
 }
+
+// CHECK-LABEL: @compare_eq
+// CHECK: ([[LHS:%.+]]: tensor<2xcomplex<f32>>, [[RHS:%.+]]: tensor<2xcomplex<f32>>)
+func @compare_eq(%lhs : tensor<2xcomplex<f32>>, %rhs: tensor<2xcomplex<f32>>) -> (tensor<2xi1>) {
+  // CHECK-DAG: [[REAL_LHS:%.+]] = "mhlo.real"([[LHS]])
+  // CHECK-DAG: [[REAL_RHS:%.+]] = "mhlo.real"([[RHS]])
+  // CHECK-DAG: [[OUTR:%.+]] = "mhlo.compare"([[REAL_LHS]], [[REAL_RHS]]) {comparison_direction = "EQ"}
+  // CHECK-DAG: [[IMAG_LHS:%.+]] = "mhlo.imag"([[LHS]])
+  // CHECK-DAG: [[IMAG_RHS:%.+]] = "mhlo.imag"([[RHS]])
+  // CHECK-DAG: [[OUTI:%.+]] = "mhlo.compare"([[IMAG_LHS]], [[IMAG_RHS]]) {comparison_direction = "EQ"}
+  // CHECK-DAG: [[OUT:%.+]] = mhlo.and [[OUTR]], [[OUTI]]
+  %0 = "mhlo.compare"(%lhs, %rhs) {comparison_direction = "EQ"} : (tensor<2xcomplex<f32>>, tensor<2xcomplex<f32>>) -> tensor<2xi1>
+
+  // CHECK: return [[OUT]]
+  return %0 : tensor<2xi1>
+}
+
+// CHECK-LABEL: @compare_ne
+// CHECK: ([[LHS:%.+]]: tensor<2xcomplex<f32>>, [[RHS:%.+]]: tensor<2xcomplex<f32>>)
+func @compare_ne(%lhs : tensor<2xcomplex<f32>>, %rhs: tensor<2xcomplex<f32>>) -> (tensor<2xi1>) {
+  // CHECK-DAG: [[REAL_LHS:%.+]] = "mhlo.real"([[LHS]])
+  // CHECK-DAG: [[REAL_RHS:%.+]] = "mhlo.real"([[RHS]])
+  // CHECK-DAG: [[OUTR:%.+]] = "mhlo.compare"([[REAL_LHS]], [[REAL_RHS]]) {comparison_direction = "NE"}
+  // CHECK-DAG: [[IMAG_LHS:%.+]] = "mhlo.imag"([[LHS]])
+  // CHECK-DAG: [[IMAG_RHS:%.+]] = "mhlo.imag"([[RHS]])
+  // CHECK-DAG: [[OUTI:%.+]] = "mhlo.compare"([[IMAG_LHS]], [[IMAG_RHS]]) {comparison_direction = "NE"}
+  // CHECK-DAG: [[OUT:%.+]] = mhlo.or [[OUTR]], [[OUTI]]
+  %0 = "mhlo.compare"(%lhs, %rhs) {comparison_direction = "NE"} : (tensor<2xcomplex<f32>>, tensor<2xcomplex<f32>>) -> tensor<2xi1>
+
+  // CHECK: return [[OUT]]
+  return %0 : tensor<2xi1>
+}