diff --git a/Lib/test/test_complex.py b/Lib/test/test_complex.py
index ecc97315e50d31..40d804ed37823a 100644
--- a/Lib/test/test_complex.py
+++ b/Lib/test/test_complex.py
@@ -338,6 +338,11 @@ def test_pow(self):
                     except OverflowError:
                         pass
 
+        # Check that complex numbers with special components
+        # are correctly handled.
+        self.assertComplexesAreIdentical(complex(1, +0.0)**2, complex(1, +0.0))
+        self.assertComplexesAreIdentical(complex(1, -0.0)**2, complex(1, -0.0))
+
     def test_pow_with_small_integer_exponents(self):
         # Check that small integer exponents are handled identically
         # regardless of their type.
diff --git a/Misc/NEWS.d/next/Library/2024-08-24-10-46-35.gh-issue-117999.5K_BiA.rst b/Misc/NEWS.d/next/Library/2024-08-24-10-46-35.gh-issue-117999.5K_BiA.rst
new file mode 100644
index 00000000000000..2e3c45ad97215f
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-08-24-10-46-35.gh-issue-117999.5K_BiA.rst
@@ -0,0 +1,2 @@
+Use a single algorithm for complex exponentiation (the case where the exponent
+is a small integer was previously handled separately).  Patch by Sergey B Kirpichev.
diff --git a/Objects/complexobject.c b/Objects/complexobject.c
index 787235c63a6be1..b996844a2029f4 100644
--- a/Objects/complexobject.c
+++ b/Objects/complexobject.c
@@ -23,8 +23,6 @@ class complex "PyComplexObject *" "&PyComplex_Type"
 
 /* elementary operations on complex numbers */
 
-static Py_complex c_1 = {1., 0.};
-
 Py_complex
 _Py_c_sum(Py_complex a, Py_complex b)
 {
@@ -179,32 +177,6 @@ _Py_c_pow(Py_complex a, Py_complex b)
     return r;
 }
 
-static Py_complex
-c_powu(Py_complex x, long n)
-{
-    Py_complex r, p;
-    long mask = 1;
-    r = c_1;
-    p = x;
-    while (mask > 0 && n >= mask) {
-        if (n & mask)
-            r = _Py_c_prod(r,p);
-        mask <<= 1;
-        p = _Py_c_prod(p,p);
-    }
-    return r;
-}
-
-static Py_complex
-c_powi(Py_complex x, long n)
-{
-    if (n > 0)
-        return c_powu(x,n);
-    else
-        return _Py_c_quot(c_1, c_powu(x,-n));
-
-}
-
 double
 _Py_c_abs(Py_complex z)
 {
@@ -565,16 +537,7 @@ complex_pow(PyObject *v, PyObject *w, PyObject *z)
         return NULL;
     }
     errno = 0;
-    // Check whether the exponent has a small integer value, and if so use
-    // a faster and more accurate algorithm.
-    if (b.imag == 0.0 && b.real == floor(b.real) && fabs(b.real) <= 100.0) {
-        p = c_powi(a, (long)b.real);
-        _Py_ADJUST_ERANGE2(p.real, p.imag);
-    }
-    else {
-        p = _Py_c_pow(a, b);
-    }
-
+    p = _Py_c_pow(a, b);
     if (errno == EDOM) {
         PyErr_SetString(PyExc_ZeroDivisionError,
                         "zero to a negative or complex power");