Fix variance calculation for complex numbers by preserving dtype

doc/source/whatsnew/v3.0.0.rst

@@ -994,6 +994,7 @@ Numeric
 - Bug in :meth:`DataFrame.quantile` where the column type was not preserved when ``numeric_only=True`` with a list-like ``q`` produced an empty result (:issue:`59035`)
 - Bug in :meth:`Series.dot` returning ``object`` dtype for :class:`ArrowDtype` and nullable-dtype data (:issue:`61375`)
 - Bug in :meth:`Series.std` and :meth:`Series.var` when using complex-valued data (:issue:`61645`)
+- Bug in :meth:`Series.var` incorrectly computing variance for complex arrays by discarding the imaginary part during mean calculation (:issue:`62421`)
 - Bug in ``np.matmul`` with :class:`Index` inputs raising a ``TypeError`` (:issue:`57079`)
 
 Conversion

pandas/core/nanops.py

@@ -1013,7 +1013,11 @@ def nanvar(
     # observations.
     #
     # See https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
-    avg = _ensure_numeric(values.sum(axis=axis, dtype=np.float64)) / count
+    if values.dtype.kind == "c":
+        # For complex numbers, preserve the dtype to avoid discarding imaginary part
+        avg = _ensure_numeric(values.sum(axis=axis, dtype=values.dtype)) / count
+    else:
+        avg = _ensure_numeric(values.sum(axis=axis, dtype=np.float64)) / count
     if axis is not None:
         avg = np.expand_dims(avg, axis)
     if values.dtype.kind == "c":

pandas/tests/reductions/test_reductions.py

@@ -787,6 +787,27 @@ def test_var_complex_array(self):
         assert ser.var(ddof=1) == 1.0
         assert ser.std(ddof=1) == 1.0
 
+    @pytest.mark.parametrize(
+        "values,ddof,expected",
+        [
+            ([1 + 2j, 2 + 3j, 3 + 4j], 1, 2.0),
+            ([1 + 2j, 2 + 3j, 3 + 4j], 0, 4 / 3),
+            ([1 + 2j, 2 + 3j, 3 + 4j, np.nan + 0j], 1, 2.0),
+        ],
+    )
+    def test_var_complex_values(self, values, ddof, expected):
+        # GH#62421
+        ser = Series(values, dtype=np.complex128)
+        result = ser.var(ddof=ddof)
+        tm.assert_almost_equal(result, expected)
+
+    def test_var_complex_dtype_preserved(self):
+        # GH#62421
+        ser = Series([1 + 2j, 2 + 3j, 3 + 4j], dtype=np.complex128)
+        mean = ser.mean()
+        assert isinstance(mean, complex)
+        assert mean == 2 + 3j
+
     @pytest.mark.parametrize("dtype", ("m8[ns]", "M8[ns]", "M8[ns, UTC]"))
     def test_empty_timeseries_reductions_return_nat(self, dtype, skipna):
         # covers GH#11245