@@ -366,6 +366,16 @@ def test_pow(self):
         self.assertRaises(TypeError, pow, None, 1j)
         self.assertAlmostEqual(pow(1j, 0.5), 0.7071067811865476+0.7071067811865475j)
 
+        # gh-156886: an infinite phase is not a zero base.
+        for base, exp in [(complex(INF), 1j),
+                          (complex(INF, 1), 1j),
+                          (1e300, 1e308j),
+                          (complex(2), complex(0, INF))]:
+            with self.subTest(base=base, exponent=exp):
+                r = base ** exp
+                self.assertTrue(isnan(r.real))
+                self.assertTrue(isnan(r.imag))
+
         a = 3.33+4.43j
         self.assertEqual(a ** 0j, 1)
         self.assertEqual(a ** 0.+0.j, 1)
 
@@ -0,0 +1,3 @@
+Fix :exc:`ZeroDivisionError` spuriously raised for a complex power
+with a non-zero base when the phase of the result is infinite,
+e.g. ``1e300**1e308j`` or ``complex('inf')**1j``.
@@ -331,6 +331,9 @@ _Py_c_pow(Py_complex a, Py_complex b)
         r.real = len*cos(phase);
         r.imag = len*sin(phase);
 
+        /* Don't rely on errno set by the math functions above, for
+           example cos() and sin() set EDOM for an infinite phase. */
+        errno = 0;
         if (isfinite(a.real) && isfinite(a.imag)
             && isfinite(b.real) && isfinite(b.imag))
         {
Original file line number	Diff line number	Diff line change
@@ -0,0 +1,3 @@
	1	+ Fix :exc:`ZeroDivisionError` spuriously raised for a complex power
	2	+ with a non-zero base when the phase of the result is infinite,
	3	+ e.g. ``1e3001e308j`` or ``complex('inf')1j``.
Original file line number	Diff line number	Diff line change
@@ -331,6 +331,9 @@ _Py_c_pow(Py_complex a, Py_complex b)
331	331	r.real = len*cos(phase);
332	332	r.imag = len*sin(phase);
333	333
	334	+ /* Don't rely on errno set by the math functions above, for
	335	+ example cos() and sin() set EDOM for an infinite phase. */
	336	+ errno = 0;
334	337	if (isfinite(a.real) && isfinite(a.imag)
335	338	&& isfinite(b.real) && isfinite(b.imag))
336	339	{