BUG: series with complex nan (pandas-dev#53682)

* avoid float(complex('nan'))

* update

* added test

* modified tests; added changelog

* changelog modified

doc/source/whatsnew/v2.1.0.rst

@@ -520,6 +520,7 @@ Metadata
 
 Other
 ^^^^^
+- Bug in :class:`DataFrame` and :class:`Series` raising for data of complex dtype when ``NaN`` values are present (:issue:`53627`)
 - Bug in :class:`FloatingArray.__contains__` with ``NaN`` item incorrectly returning ``False`` when ``NaN`` values are present (:issue:`52840`)
 - Bug in :func:`api.interchange.from_dataframe` when converting an empty DataFrame object (:issue:`53155`)
 - Bug in :func:`assert_almost_equal` now throwing assertion error for two unequal sets (:issue:`51727`)

pandas/_libs/lib.pyx

@@ -2485,7 +2485,14 @@ def maybe_convert_objects(ndarray[object] objects,
         elif util.is_nan(val):
             seen.nan_ = True
             mask[i] = True
-            floats[i] = complexes[i] = val
+            if util.is_complex_object(val):
+                floats[i] = fnan
+                complexes[i] = val
+                seen.complex_ = True
+                if not convert_numeric:
+                    break
+            else:
+                floats[i] = complexes[i] = val
         elif util.is_bool_object(val):
             seen.bool_ = True
             bools[i] = val

pandas/tests/series/test_constructors.py

@@ -2154,3 +2154,18 @@ def test_index_ordered_dict_keys():
         ),
     )
     tm.assert_series_equal(series, expected)
+
+
+@pytest.mark.parametrize(
+    "input_list",
+    [
+        [1, complex("nan"), 2],
+        [1 + 1j, complex("nan"), 2 + 2j],
+    ],
+)
+def test_series_with_complex_nan(input_list):
+    # GH#53627
+    ser = Series(input_list)
+    result = Series(ser.array)
+    assert ser.dtype == "complex128"
+    tm.assert_series_equal(ser, result)