fix std/var with complex array (pandas-dev#61646)

* fix std/var with complex array

* added whatsnew entry

Author: randolf-scholz

doc/source/whatsnew/v3.0.0.rst

@@ -716,6 +716,7 @@ Numeric
 - Bug in :meth:`DataFrame.cov` raises a ``TypeError`` instead of returning potentially incorrect results or other errors (:issue:`53115`)
 - 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 ``np.matmul`` with :class:`Index` inputs raising a ``TypeError`` (:issue:`57079`)
 
 Conversion

pandas/core/nanops.py

@@ -1014,7 +1014,11 @@ def nanvar(
     avg = _ensure_numeric(values.sum(axis=axis, dtype=np.float64)) / count
     if axis is not None:
         avg = np.expand_dims(avg, axis)
-    sqr = _ensure_numeric((avg - values) ** 2)
+    if values.dtype.kind == "c":
+        # Need to use absolute value for complex numbers.
+        sqr = _ensure_numeric(abs(avg - values) ** 2)
+    else:
+        sqr = _ensure_numeric((avg - values) ** 2)
     if mask is not None:
         np.putmask(sqr, mask, 0)
     result = sqr.sum(axis=axis, dtype=np.float64) / d

pandas/tests/reductions/test_reductions.py

@@ -780,6 +780,12 @@ def test_var_masked_array(self, ddof, exp):
         assert result == result_numpy_dtype
         assert result == exp
 
+    def test_var_complex_array(self):
+        # GH#61645
+        ser = Series([-1j, 0j, 1j], dtype=complex)
+        assert ser.var(ddof=1) == 1.0
+        assert ser.std(ddof=1) == 1.0
+
     @pytest.mark.parametrize("dtype", ("m8[ns]", "M8[ns]", "M8[ns, UTC]"))
     def test_empty_timeseries_reductions_return_nat(self, dtype, skipna):
         # covers GH#11245