diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index f87dac0669e00..6c4bd35c8f183 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -276,6 +276,7 @@ Numeric
 - Bug in :meth:`DataFrame.any` with ``axis=1`` and ``bool_only=True`` ignoring the ``bool_only`` keyword (:issue:`32432`)
 - Bug in :meth:`Series.equals` where a ``ValueError`` was raised when numpy arrays were compared to scalars (:issue:`35267`)
 - Bug in :class:`Series` where two :class:`Series` each have a :class:`DatetimeIndex` with different timezones having those indexes incorrectly changed when performing arithmetic operations (:issue:`33671`)
+- Bug in :meth:`pd._testing.assert_almost_equal` was incorrect for complex numeric types (:issue:`28235`)
 -
 
 Conversion
diff --git a/pandas/_libs/testing.pyx b/pandas/_libs/testing.pyx
index 64fc8d615ea9c..b2f19fcf5f5da 100644
--- a/pandas/_libs/testing.pyx
+++ b/pandas/_libs/testing.pyx
@@ -1,3 +1,4 @@
+import cmath
 import math
 
 import numpy as np
@@ -7,6 +8,7 @@ from numpy cimport import_array
 import_array()
 
 from pandas._libs.util cimport is_array
+from pandas._libs.lib import is_complex
 
 from pandas.core.dtypes.common import is_dtype_equal
 from pandas.core.dtypes.missing import array_equivalent, isna
@@ -210,4 +212,14 @@ cpdef assert_almost_equal(a, b,
                            f"with rtol={rtol}, atol={atol}")
         return True
 
+    if is_complex(a) and is_complex(b):
+        if array_equivalent(a, b, strict_nan=True):
+            # inf comparison
+            return True
+
+        if not cmath.isclose(a, b, rel_tol=rtol, abs_tol=atol):
+            assert False, (f"expected {b:.5f} but got {a:.5f}, "
+                           f"with rtol={rtol}, atol={atol}")
+        return True
+
     raise AssertionError(f"{a} != {b}")
diff --git a/pandas/tests/util/test_assert_almost_equal.py b/pandas/tests/util/test_assert_almost_equal.py
index c25668c33bfc4..c4bc3b7ee352d 100644
--- a/pandas/tests/util/test_assert_almost_equal.py
+++ b/pandas/tests/util/test_assert_almost_equal.py
@@ -146,6 +146,37 @@ def test_assert_not_almost_equal_numbers_rtol(a, b):
     _assert_not_almost_equal_both(a, b, rtol=0.05)
 
 
+@pytest.mark.parametrize(
+    "a,b,rtol",
+    [
+        (1.00001, 1.00005, 0.001),
+        (-0.908356 + 0.2j, -0.908358 + 0.2j, 1e-3),
+        (0.1 + 1.009j, 0.1 + 1.006j, 0.1),
+        (0.1001 + 2.0j, 0.1 + 2.001j, 0.01),
+    ],
+)
+def test_assert_almost_equal_complex_numbers(a, b, rtol):
+    _assert_almost_equal_both(a, b, rtol=rtol)
+    _assert_almost_equal_both(np.complex64(a), np.complex64(b), rtol=rtol)
+    _assert_almost_equal_both(np.complex128(a), np.complex128(b), rtol=rtol)
+
+
+@pytest.mark.parametrize(
+    "a,b,rtol",
+    [
+        (0.58310768, 0.58330768, 1e-7),
+        (-0.908 + 0.2j, -0.978 + 0.2j, 0.001),
+        (0.1 + 1j, 0.1 + 2j, 0.01),
+        (-0.132 + 1.001j, -0.132 + 1.005j, 1e-5),
+        (0.58310768j, 0.58330768j, 1e-9),
+    ],
+)
+def test_assert_not_almost_equal_complex_numbers(a, b, rtol):
+    _assert_not_almost_equal_both(a, b, rtol=rtol)
+    _assert_not_almost_equal_both(np.complex64(a), np.complex64(b), rtol=rtol)
+    _assert_not_almost_equal_both(np.complex128(a), np.complex128(b), rtol=rtol)
+
+
 @pytest.mark.parametrize("a,b", [(0, 0), (0, 0.0), (0, np.float64(0)), (0.00000001, 0)])
 def test_assert_almost_equal_numbers_with_zeros(a, b):
     _assert_almost_equal_both(a, b)