diff --git a/Lib/test/test_cmath.py b/Lib/test/test_cmath.py
index a986fd6b892bd2..b736b2b75a3db4 100644
--- a/Lib/test/test_cmath.py
+++ b/Lib/test/test_cmath.py
@@ -590,6 +590,16 @@ def test_complex_special(self):
         self.assertIsNotClose(-INF, INF)
         self.assertIsNotClose(0, INF)
         self.assertIsNotClose(0, INF*1j)
+        for z in complex_nans:
+            for w in complex_infinities + complex_nans:
+                self.assertIsNotClose(z, w)
+
+        for z in complex_infinities:
+            for w in complex_infinities:
+                if z != w:
+                    self.assertIsNotClose(z, w)
+                else:
+                    self.assertIsClose(z, z)
 
 
 if __name__ == "__main__":