diff --git a/mlir/lib/Conversion/ComplexToLibm/ComplexToLibm.cpp b/mlir/lib/Conversion/ComplexToLibm/ComplexToLibm.cpp
--- a/mlir/lib/Conversion/ComplexToLibm/ComplexToLibm.cpp
+++ b/mlir/lib/Conversion/ComplexToLibm/ComplexToLibm.cpp
@@ -77,6 +77,8 @@
                                                    "ccosf", "ccos", benefit);
   patterns.add<ScalarOpToLibmCall<complex::SinOp>>(patterns.getContext(),
                                                    "csinf", "csin", benefit);
+  patterns.add<ScalarOpToLibmCall<complex::ConjOp>>(patterns.getContext(),
+                                                    "conjf", "conj", benefit);
 }
 
 namespace {
diff --git a/mlir/test/Conversion/ComplexToLibm/convert-to-libm.mlir b/mlir/test/Conversion/ComplexToLibm/convert-to-libm.mlir
--- a/mlir/test/Conversion/ComplexToLibm/convert-to-libm.mlir
+++ b/mlir/test/Conversion/ComplexToLibm/convert-to-libm.mlir
@@ -8,6 +8,7 @@
 // CHECK-DAG: @ctanh(complex<f64>) -> complex<f64>
 // CHECK-DAG: @ccos(complex<f64>) -> complex<f64>
 // CHECK-DAG: @csin(complex<f64>) -> complex<f64>
+// CHECK-DAG: @conj(complex<f64>) -> complex<f64>
 
 // CHECK-LABEL: func @cpow_caller
 // CHECK-SAME: %[[FLOAT:.*]]: complex<f32>
@@ -67,4 +68,16 @@
   %double_result = complex.sin %double : complex<f64>
   // CHECK: return %[[FLOAT_RESULT]], %[[DOUBLE_RESULT]]
   return %float_result, %double_result : complex<f32>, complex<f64>
+}
+
+// CHECK-LABEL: func @conj_caller
+// CHECK-SAME: %[[FLOAT:.*]]: complex<f32>
+// CHECK-SAME: %[[DOUBLE:.*]]: complex<f64>
+func.func @conj_caller(%float: complex<f32>, %double: complex<f64>) -> (complex<f32>, complex<f64>)  {
+  // CHECK: %[[FLOAT_RESULT:.*]] = call @conjf(%[[FLOAT]])
+  %float_result = complex.conj %float : complex<f32>
+  // CHECK: %[[DOUBLE_RESULT:.*]] = call @conj(%[[DOUBLE]])
+  %double_result = complex.conj %double : complex<f64>
+  // CHECK: return %[[FLOAT_RESULT]], %[[DOUBLE_RESULT]]
+  return %float_result, %double_result : complex<f32>, complex<f64>
 }
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