diff --git a/tests/test_decoder.py b/tests/test_decoder.py
index 84ef1d7..248e915 100644
--- a/tests/test_decoder.py
+++ b/tests/test_decoder.py
@@ -538,6 +538,33 @@ def test_bigfloat(impl):
     decoded = impl.loads(unhexlify("c5822003"))
     assert decoded == Decimal("1.5")
 
+@pytest.mark.parametrize(
+    "payload, expected",
+    [
+        ("d9a7f882f90000f90000", 0.0j),
+        ("d9a7f882fb0000000000000000fb0000000000000000", 0.0j),
+        ("d9a7f882f98000f98000", -0.0j),
+        ("d9a7f882f90000f93c00", 1.0j),
+        ("d9a7f882fb0000000000000000fb3ff199999999999a", 1.1j),
+        ("d9a7f882f93e00f93e00", 1.5+1.5j),
+        ("d9a7f882f97bfff97bff", 65504.0+65504.0j),
+        ("d9a7f882fa47c35000fa47c35000", 100000.0+100000.0j),
+        ("fa7f7fffff", 3.4028234663852886e38),
+        ("d9a7f882f90000fb7e37e43c8800759c", 1.0e300j),
+        ("d9a7f882f90000f90001", 5.960464477539063e-8j),
+        ("d9a7f882f90000f90400", 0.00006103515625j),
+        ("d9a7f882f90000f9c400", -4.0j),
+        ("d9a7f882f90000fbc010666666666666", -4.1j),
+        ("d9a7f882f90000f97c00", complex(0.0, float("inf"))),
+        ("d9a7f882f97c00f90000", complex(float("inf"), 0.0)),
+        ("d9a7f882f90000f9fc00", complex(0.0, float("-inf"))),
+        ("d9a7f882f90000fa7f800000", complex(0.0, float("inf"))),
+        ("d9a7f882f90000faff800000", complex(0.0, float("-inf"))),
+    ],
+)
+def test_complex(impl, payload, expected):
+    decoded = impl.loads(unhexlify(payload))
+    assert decoded == expected
 
 def test_rational(impl):
     decoded = impl.loads(unhexlify("d81e820205"))
diff --git a/tests/test_encoder.py b/tests/test_encoder.py
index f2ef248..715c81e 100644
--- a/tests/test_encoder.py
+++ b/tests/test_encoder.py
@@ -324,6 +324,21 @@ def test_decimal(impl, value, expected):
     assert impl.dumps(value) == expected
 
 
+@pytest.mark.parametrize(
+    "value, expected",
+    [
+        (3.1 + 2.1j, "d9a7f882fb4008cccccccccccdfb4000cccccccccccd"),
+        (1.0e300j, "d9a7f882fb0000000000000000fb7e37e43c8800759c"),
+        (0.0j, "d9a7f882fb0000000000000000fb0000000000000000"),
+        (complex(float("inf"), float("inf")), "d9a7f882f97c00f97c00"),
+        (complex(float("inf"), 0.0), "d9a7f882f97c00fb0000000000000000"),
+        (complex(float("nan"), float("inf")), "d9a7f882f97e00f97c00"),
+    ],
+)
+def test_complex(impl, value, expected):
+    expected = unhexlify(expected)
+    assert impl.dumps(value) == expected
+
 def test_rational(impl):
     expected = unhexlify("d81e820205")
     assert impl.dumps(Fraction(2, 5)) == expected