diff --git a/core/integer.rbs b/core/integer.rbs
index 76a5616bf..f20d26d39 100644
--- a/core/integer.rbs
+++ b/core/integer.rbs
@@ -1028,9 +1028,10 @@ class Integer < Numeric
   #     a.pow(b)     #=> same as a**b
   #     a.pow(b, m)  #=> same as (a**b) % m, but avoids huge temporary values
   #
-  def pow: (Integer other, ?Integer modulo) -> Integer
-         | (Float) -> Float
-         | (Rational) -> Rational
+  def pow: (Integer other) -> (Integer | Rational)
+         | (Integer other, Integer modulo) -> Integer
+         | (Float) -> (Float | Complex)
+         | (Rational) -> (Float | Rational | Complex)
          | (Complex) -> Complex
 
   # <!--
diff --git a/test/stdlib/Integer_test.rb b/test/stdlib/Integer_test.rb
index b4661c2d7..973885bdb 100644
--- a/test/stdlib/Integer_test.rb
+++ b/test/stdlib/Integer_test.rb
@@ -369,3 +369,30 @@ def test_try_convert
     )
   end
 end
+
+class IntegerInstanceTest < Test::Unit::TestCase
+  include TestHelper
+
+  testing "::Integer"
+
+  def test_pow
+    assert_send_type "(Integer) -> Integer",
+                     1, :pow, 2
+    assert_send_type "(Integer) -> Rational",
+                     -2, :pow, -1
+    assert_send_type "(Integer, Integer) -> Integer",
+                     1, :pow, 2, 10
+    assert_send_type "(Float) -> Float",
+                     1, :pow, 1.0
+    assert_send_type "(Float) -> Complex",
+                     -9, :pow, 0.1
+    assert_send_type "(Rational) -> Float",
+                     2, :pow, 1/2r
+    assert_send_type "(Rational) -> Rational",
+                     1, :pow, 1r
+    assert_send_type "(Rational) -> Complex",
+                     -3, :pow, -4/3r
+    assert_send_type "(Complex) -> Complex",
+                     1, :pow, 1i
+  end
+end