BUG: Fix infer_dtype result for complex with pd.NA (#61977)

Co-authored-by: XY <yuanx749@outlook.com>

Author: yuanx749

doc/source/whatsnew/v3.0.0.rst

@@ -731,6 +731,7 @@ Timezones
 
 Numeric
 ^^^^^^^
+- Bug in :func:`api.types.infer_dtype` returning "mixed" for complex and ``pd.NA`` mix (:issue:`61976`)
 - Bug in :func:`api.types.infer_dtype` returning "mixed-integer-float" for float and ``pd.NA`` mix (:issue:`61621`)
 - Bug in :meth:`DataFrame.corr` where numerical precision errors resulted in correlations above ``1.0`` (:issue:`61120`)
 - Bug in :meth:`DataFrame.cov` raises a ``TypeError`` instead of returning potentially incorrect results or other errors (:issue:`53115`)

pandas/_libs/lib.pyx

@@ -1974,9 +1974,11 @@ cdef class ComplexValidator(Validator):
         return cnp.PyDataType_ISCOMPLEX(self.dtype)
 
 
-cdef bint is_complex_array(ndarray values):
+cdef bint is_complex_array(ndarray values, bint skipna=True):
     cdef:
-        ComplexValidator validator = ComplexValidator(values.size, values.dtype)
+        ComplexValidator validator = ComplexValidator(values.size,
+                                                      values.dtype,
+                                                      skipna=skipna)
     return validator.validate(values)
 
 

pandas/tests/dtypes/test_inference.py

@@ -1405,6 +1405,10 @@ def test_infer_dtype_numeric_with_na(self, na_value):
         ser = Series([1.0, 2.0, na_value], dtype=object)
         assert lib.infer_dtype(ser, skipna=True) == "floating"
 
+        # GH#61976
+        ser = Series([1 + 1j, na_value], dtype=object)
+        assert lib.infer_dtype(ser, skipna=True) == "complex"
+
     def test_infer_dtype_all_nan_nat_like(self):
         arr = np.array([np.nan, np.nan])
         assert lib.infer_dtype(arr, skipna=True) == "floating"