diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 21d12d02c9008..c795a1452ade2 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -4,7 +4,7 @@
 """
 from textwrap import dedent
 from typing import Dict
-from warnings import catch_warnings, simplefilter, warn
+from warnings import warn
 
 import numpy as np
 
@@ -101,13 +101,7 @@ def _ensure_data(values, dtype=None):
         elif is_object_dtype(values) and dtype is None:
             return ensure_object(np.asarray(values)), "object", "object"
         elif is_complex_dtype(values) or is_complex_dtype(dtype):
-
-            # ignore the fact that we are casting to float
-            # which discards complex parts
-            with catch_warnings():
-                simplefilter("ignore", np.ComplexWarning)
-                values = ensure_float64(values)
-            return values, "float64", "float64"
+            raise TypeError("Complex data types not supported...Coercing to object")
 
     except (TypeError, ValueError, OverflowError):
         # if we are trying to coerce to a dtype
diff --git a/pandas/tests/test_complex.py b/pandas/tests/test_complex.py
new file mode 100644
index 0000000000000..9afe8c476f5ca
--- /dev/null
+++ b/pandas/tests/test_complex.py
@@ -0,0 +1,125 @@
+import numpy as np
+import pytest
+
+import pandas as pd
+from pandas import DataFrame, Index, Series
+import pandas.core.algorithms as algos
+import pandas.util.testing as tm
+
+
+class TestBasicComplexSupport:
+    @pytest.mark.parametrize(
+        "array,expected",
+        [
+            (
+                [1 + 1j, 0, 1, 1j, 1 + 2j],
+                Series([1, 1, 1, 1, 1], index=[1 + 2j, 1 + 1j, 1j, 1, 0]),
+            ),
+            (
+                [1 + 2j, 0, 1j, 1, 1j, 1 + 1j],
+                # index is sorted by value counts in descending order by default
+                Series([2, 1, 1, 1, 1], index=[1j, 1 + 2j, 1 + 1j, 1, 0]),
+            ),
+        ],
+    )
+    def test_value_counts(self, array, expected):
+        result = algos.value_counts(array)
+        tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "array,expected",
+        [
+            (
+                [1 + 1j, 0, 1, 1j, 1 + 2j, 1 + 2j],
+                np.array([(1 + 1j), 0j, (1 + 0j), 1j, (1 + 2j)], dtype=object),
+            )
+        ],
+    )
+    def test_unique(self, array, expected):
+        result = algos.unique(array)
+        tm.assert_numpy_array_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "array,expected",
+        [
+            (
+                [0, 1j, 1j, 1, 1 + 1j, 1 + 2j, 1 + 1j],
+                Series([False, False, True, False, False, False, True], dtype=bool),
+            )
+        ],
+    )
+    def test_duplicated(self, array, expected):
+        result = Series(array).duplicated()
+        tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "array,expected",
+        [
+            (
+                [0, 1j, 1j, 1, 1 + 1j, 1 + 2j, 1 + 1j],
+                Series([False, True, True, False, True, True, True], dtype=bool),
+            )
+        ],
+    )
+    def test_isin(self, array, expected):
+        result = Series(array).isin([1j, 1 + 1j, 1 + 2j])
+        tm.assert_series_equal(result, expected)
+
+    def test_factorize(self):
+        array = [1, 2, 2 + 1j]
+        labels, uniques = pd.factorize(array)
+        expected = np.array([0, 1, 2], dtype=np.intp)
+        tm.assert_numpy_array_equal(labels, expected)
+        expected = np.array([(1 + 0j), (2 + 0j), (2 + 1j)], dtype=object)
+        tm.assert_numpy_array_equal(uniques, expected)
+
+    @pytest.mark.parametrize(
+        "frame,expected",
+        [
+            (
+                DataFrame([dict(a=1, b=1 + 1j), dict(a=1, b=1 + 2j)]),
+                DataFrame(
+                    np.array([1, 1], dtype=np.int64),
+                    index=Index([(1 + 1j), (1 + 2j)], dtype="object", name="b"),
+                    columns=Index(["a"], dtype="object"),
+                ),
+            )
+        ],
+    )
+    def test_groupby(self, frame, expected):
+        result = frame.groupby("b", sort=False).count()
+        tm.assert_frame_equal(result, expected)
+
+        # sorting of the index should fail since complex numbers are unordered
+        with pytest.raises(TypeError):
+            frame.groupby("b", sort=True).count()
+
+    @pytest.mark.parametrize(
+        "array,expected",
+        [
+            ([0, 1j, 1, 1, 1 + 1j, 1 + 2j], Series([1], dtype=np.complex128)),
+            ([1 + 1j, 2j, 1 + 1j], Series([1 + 1j], dtype=np.complex128)),
+        ],
+    )
+    def test_unimode(self, array, expected):
+        result = Series(array).mode()
+        tm.assert_series_equal(result, expected)
+
+    # mode tries to sort multimodal series.
+    # A warning will be raised since complex numbers
+    # are not ordered.
+    @pytest.mark.parametrize(
+        "array,expected",
+        [
+            (
+                # no modes
+                [0, 1j, 1, 1 + 1j, 1 + 2j],
+                Series([0, 1, 1j, 1 + 1j, 1 + 2j], dtype=np.complex128),
+            ),
+            ([1 + 1j, 2j, 1 + 1j, 2j, 3], Series([1 + 1j, 2j], dtype=np.complex128)),
+        ],
+    )
+    def test_multimode(self, array, expected):
+        with tm.assert_produces_warning(UserWarning):
+            result = Series(array).mode()
+        tm.assert_series_equal(result, expected)