diff --git a/core/complex.rbs b/core/complex.rbs
index 5126ab086..864d4e057 100644
--- a/core/complex.rbs
+++ b/core/complex.rbs
@@ -377,7 +377,7 @@ class Complex < Numeric
   #
   #     Complex.rect(1, 2).conj # => (1-2i)
   #
-  def conj: () -> Complex
+  def conj: () -> self
 
   # <!--
   #   rdoc-file=complex.c
@@ -387,7 +387,7 @@ class Complex < Numeric
   #
   #     Complex.rect(1, 2).conj # => (1-2i)
   #
-  def conjugate: () -> Complex
+  def conjugate: () -> self
 
   # <!--
   #   rdoc-file=complex.c
@@ -522,8 +522,6 @@ class Complex < Numeric
   #
   def inspect: () -> String
 
-  def integer?: () -> bool
-
   # <!-- rdoc-file=complex.c -->
   # Returns the absolute value (magnitude) for `self`; see [polar
   # coordinates](rdoc-ref:Complex@Polar+Coordinates):
@@ -745,8 +743,6 @@ class Complex < Numeric
   #
   def to_i: () -> Integer
 
-  alias to_int to_i
-
   # <!--
   #   rdoc-file=complex.c
   #   - to_r -> rational
@@ -779,8 +775,6 @@ class Complex < Numeric
   def to_s: () -> String
 
   def truncate: (?Integer) -> bot
-
-  def zero?: () -> bool
 end
 
 # <!-- rdoc-file=complex.c -->
diff --git a/core/float.rbs b/core/float.rbs
index 0674b4a08..f96c403ad 100644
--- a/core/float.rbs
+++ b/core/float.rbs
@@ -324,12 +324,10 @@ class Float < Numeric
   #
   def abs: () -> Float
 
-  def abs2: () -> Float
-
   # <!-- rdoc-file=complex.c -->
   # Returns 0 if `self` is positive, Math::PI otherwise.
   #
-  def angle: () -> (Integer | Float)
+  def angle: ...
 
   # <!--
   #   rdoc-file=complex.c
@@ -417,10 +415,6 @@ class Float < Numeric
   #
   def coerce: (Numeric) -> [ Float, Float ]
 
-  def conj: () -> Float
-
-  def conjugate: () -> Float
-
   # <!--
   #   rdoc-file=rational.c
   #   - flo.denominator  ->  integer
@@ -431,8 +425,6 @@ class Float < Numeric
   #
   def denominator: () -> Integer
 
-  def div: (Numeric) -> Integer
-
   # <!--
   #   rdoc-file=numeric.c
   #   - divmod(other) -> array
@@ -626,8 +618,6 @@ class Float < Numeric
   #
   alias inspect to_s
 
-  def integer?: () -> bool
-
   # <!--
   #   rdoc-file=numeric.rb
   #   - magnitude()
@@ -823,14 +813,8 @@ class Float < Numeric
   #
   def rationalize: (?Numeric eps) -> Rational
 
-  def real: () -> Float
-
-  def real?: () -> true
-
   def rect: () -> [ Float, Numeric ]
 
-  alias rectangular rect
-
   def remainder: (Numeric) -> Float
 
   # <!--
@@ -893,8 +877,6 @@ class Float < Numeric
           | (?by: Numeric, ?to: Numeric) { (Float) -> void } -> self
           | (?by: Numeric, ?to: Numeric) -> Enumerator[Float, self]
 
-  def to_c: () -> Complex
-
   # <!--
   #   rdoc-file=numeric.rb
   #   - to_f -> self
diff --git a/core/integer.rbs b/core/integer.rbs
index fed03a95d..81588d3b9 100644
--- a/core/integer.rbs
+++ b/core/integer.rbs
@@ -513,8 +513,6 @@ class Integer < Numeric
   #
   def abs: () -> Integer
 
-  def abs2: () -> Integer
-
   # <!--
   #   rdoc-file=numeric.c
   #   - allbits?(mask) -> true or false
@@ -538,8 +536,6 @@ class Integer < Numeric
   #
   def allbits?: (int mask) -> bool
 
-  def angle: () -> (Integer | Float)
-
   # <!--
   #   rdoc-file=numeric.c
   #   - anybits?(mask) -> true or false
@@ -704,10 +700,6 @@ class Integer < Numeric
   #
   def coerce: (Numeric) -> [ Numeric, Numeric ]
 
-  def conj: () -> Integer
-
-  def conjugate: () -> Integer
-
   # <!--
   #   rdoc-file=numeric.rb
   #   - denominator -> 1
@@ -823,8 +815,6 @@ class Integer < Numeric
   #
   def fdiv: (Numeric) -> Float
 
-  def finite?: () -> bool
-
   # <!--
   #   rdoc-file=numeric.c
   #   - floor(ndigits = 0) -> integer
@@ -895,8 +885,6 @@ class Integer < Numeric
   #
   def gcdlcm: (Integer) -> [ Integer, Integer ]
 
-  def infinite?: () -> Integer?
-
   # <!-- rdoc-file=numeric.c -->
   # Returns a string containing the place-value representation of `self` in radix
   # `base` (in 2..36).
@@ -1027,8 +1015,6 @@ class Integer < Numeric
   #
   def ord: () -> Integer
 
-  alias phase angle
-
   def polar: () -> [ Integer, Integer | Float ]
 
   def positive?: () -> bool
@@ -1077,14 +1063,8 @@ class Integer < Numeric
   #
   def rationalize: (?Numeric eps) -> Rational
 
-  def real: () -> self
-
-  def real?: () -> true
-
   def rect: () -> [ Integer, Numeric ]
 
-  alias rectangular rect
-
   # <!--
   #   rdoc-file=numeric.c
   #   - remainder(other) -> real_number
@@ -1215,8 +1195,6 @@ class Integer < Numeric
   def times: () { (Integer) -> void } -> self
            | () -> ::Enumerator[Integer, self]
 
-  def to_c: () -> Complex
-
   # <!--
   #   rdoc-file=numeric.c
   #   - to_f -> float
diff --git a/core/numeric.rbs b/core/numeric.rbs
index c62057af0..46231c55c 100644
--- a/core/numeric.rbs
+++ b/core/numeric.rbs
@@ -244,12 +244,12 @@ class Numeric
   # -->
   # Returns the square of `self`.
   #
-  def abs2: () -> Numeric
+  def abs2: () -> self
 
   # <!-- rdoc-file=complex.c -->
   # Returns zero if `self` is positive, Math::PI otherwise.
   #
-  def angle: () -> Numeric
+  def angle: () -> (0 | Float)
 
   # <!--
   #   rdoc-file=complex.c
@@ -310,18 +310,18 @@ class Numeric
 
   # <!--
   #   rdoc-file=numeric.rb
-  #   - conj()
+  #   - conj -> self
   # -->
+  # Returns `self`.
   #
-  def conj: () -> Numeric
+  def conjugate: () -> self
 
   # <!--
   #   rdoc-file=numeric.rb
-  #   - conj -> self
+  #   - conj()
   # -->
-  # Returns `self`.
   #
-  def conjugate: () -> Numeric
+  alias conj conjugate
 
   # <!--
   #   rdoc-file=rational.c
@@ -590,7 +590,7 @@ class Numeric
   # -->
   # Returns `self`.
   #
-  def real: () -> Numeric
+  def real: () -> self
 
   # <!--
   #   rdoc-file=numeric.rb
@@ -598,7 +598,7 @@ class Numeric
   # -->
   # Returns `true` if `self` is a real number (i.e. not Complex).
   #
-  def real?: () -> bool
+  def real?: () -> true
 
   # <!-- rdoc-file=complex.c -->
   # Returns array `[self, 0]`.
diff --git a/core/rational.rbs b/core/rational.rbs
index d4ac6b757..7dd2bf13c 100644
--- a/core/rational.rbs
+++ b/core/rational.rbs
@@ -186,12 +186,6 @@ class Rational < Numeric
   #
   def abs: () -> Rational
 
-  def abs2: () -> Rational
-
-  def angle: () -> (Integer | Float)
-
-  alias arg angle
-
   # <!--
   #   rdoc-file=rational.c
   #   - rat.ceil([ndigits])  ->  integer or rational
@@ -220,10 +214,6 @@ class Rational < Numeric
 
   def coerce: (Numeric) -> [ Numeric, Numeric ]
 
-  def conj: () -> Rational
-
-  def conjugate: () -> Rational
-
   # <!--
   #   rdoc-file=rational.c
   #   - rat.denominator  ->  integer
@@ -237,8 +227,6 @@ class Rational < Numeric
   #
   def denominator: () -> Integer
 
-  def div: (Numeric) -> Integer
-
   def divmod: (Integer | Float | Rational) -> [ Integer, Rational ]
             | (Numeric) -> [ Numeric, Numeric ]
 
@@ -254,8 +242,6 @@ class Rational < Numeric
   #
   def fdiv: (Numeric) -> Float
 
-  def finite?: () -> bool
-
   # <!--
   #   rdoc-file=rational.c
   #   - rat.floor([ndigits])  ->  integer or rational
@@ -289,8 +275,6 @@ class Rational < Numeric
   #
   def hash: () -> Integer
 
-  def infinite?: () -> Integer?
-
   # <!--
   #   rdoc-file=rational.c
   #   - rat.inspect  ->  string
@@ -303,8 +287,6 @@ class Rational < Numeric
   #
   def inspect: () -> String
 
-  def integer?: () -> bool
-
   # <!-- rdoc-file=rational.c -->
   # Returns the absolute value of `rat`.
   #
@@ -337,8 +319,6 @@ class Rational < Numeric
   #
   def numerator: () -> Integer
 
-  alias phase angle
-
   def polar: () -> [ Rational, Integer | Float ]
 
   # <!--
@@ -377,14 +357,8 @@ class Rational < Numeric
   #
   def rationalize: (?Numeric eps) -> Rational
 
-  def real: () -> Rational
-
-  def real?: () -> true
-
   def rect: () -> [ Rational, Numeric ]
 
-  alias rectangular rect
-
   def remainder: (Float) -> Float
                | (Numeric) -> Rational
 
@@ -431,8 +405,6 @@ class Rational < Numeric
           | (?by: Numeric, ?to: Numeric) { (Rational) -> void } -> self
           | (?by: Numeric, ?to: Numeric) -> Enumerator[Rational, self]
 
-  def to_c: () -> Complex
-
   # <!--
   #   rdoc-file=rational.c
   #   - rat.to_f  ->  float
@@ -462,8 +434,6 @@ class Rational < Numeric
   #
   def to_i: () -> Integer
 
-  alias to_int to_i
-
   # <!--
   #   rdoc-file=rational.c
   #   - rat.to_r  ->  self
@@ -512,6 +482,4 @@ class Rational < Numeric
   #
   def truncate: () -> Integer
               | (Integer ndigits) -> (Integer | Rational)
-
-  def zero?: () -> bool
 end
diff --git a/test/stdlib/Complex_test.rb b/test/stdlib/Complex_test.rb
index c8b00f206..03e0db7da 100644
--- a/test/stdlib/Complex_test.rb
+++ b/test/stdlib/Complex_test.rb
@@ -130,3 +130,22 @@ def test_rationalize
     a.rationalize(3.11)
   end
 end
+
+class ComplexInstanceTest < Test::Unit::TestCase
+  include TestHelper
+
+  testing 'Complex'
+
+  def test_real
+    assert_send_type '() -> Integer', Complex(1, 2), :real
+  end
+
+  def test_real?
+    assert_send_type '() -> false', Complex(1, 2), :real?
+  end
+
+  def test_abs2
+    assert_send_type '() -> Integer', Complex(1, 2), :abs2
+    assert_send_type '() -> Float', Complex.polar(2, 2), :abs2
+  end
+end
diff --git a/test/stdlib/Float_test.rb b/test/stdlib/Float_test.rb
index b5ef4b79e..4981ac9e2 100644
--- a/test/stdlib/Float_test.rb
+++ b/test/stdlib/Float_test.rb
@@ -79,13 +79,6 @@ def test_coerce
     2.5.coerce(1.1)
   end
 
-  def test_conj
-    a = 31.4
-
-    a.conj
-    a.conjugate
-  end
-
   def test_denominator
     a = 13.3
 
diff --git a/test/stdlib/Integer_test.rb b/test/stdlib/Integer_test.rb
index 1b22893e5..79d4d1c7f 100644
--- a/test/stdlib/Integer_test.rb
+++ b/test/stdlib/Integer_test.rb
@@ -182,10 +182,6 @@ def test_conj
     3.conj
   end
 
-  def test_conjugate
-    3.conjugate
-  end
-
   def test_denominator
     3.denominator
   end
@@ -241,10 +237,6 @@ def test_gcdlcm
     30.gcdlcm(31)
   end
 
-  def test_infinite?
-    30.infinite?
-  end
-
   def test_lcm
     30.lcm(50)
   end
diff --git a/test/stdlib/Numeric_test.rb b/test/stdlib/Numeric_test.rb
new file mode 100644
index 000000000..58db4b3e3
--- /dev/null
+++ b/test/stdlib/Numeric_test.rb
@@ -0,0 +1,42 @@
+require_relative "test_helper"
+
+class NumericInstanceTest < Test::Unit::TestCase
+  include TestHelper
+
+  testing 'Numeric'
+
+  def test_real
+    assert_send_type '() -> Integer', 1, :real
+    assert_send_type '() -> Float', 1.0, :real
+    assert_send_type '() -> Rational', 1r, :real
+  end
+
+  def test_real?
+    assert_send_type '() -> true', 1, :real?
+    assert_send_type '() -> true', 1.0, :real?
+    assert_send_type '() -> true', 1r, :real?
+  end
+
+  def test_zero?
+    assert_send_type '() -> bool', 0, :zero?
+    assert_send_type '() -> bool', 1r, :zero?
+  end
+
+  def test_angle
+    assert_send_type '() -> 0', 1, :angle
+    assert_send_type '() -> Float', -1, :angle
+    assert_send_type '() -> Float', Float::NAN, :angle
+  end
+
+  def test_abs2
+    assert_send_type '() -> Integer', 1, :abs2
+    assert_send_type '() -> Float', 1.0, :abs2
+    assert_send_type '() -> Rational', 1r, :abs2
+  end
+
+  def test_to_c
+    assert_send_type '() -> Complex', 1, :to_c
+    assert_send_type '() -> Complex', 1.0, :to_c
+    assert_send_type '() -> Complex', 1r, :to_c
+  end
+end
diff --git a/test/stdlib/Rational_test.rb b/test/stdlib/Rational_test.rb
index 94573e14a..6dba75f70 100644
--- a/test/stdlib/Rational_test.rb
+++ b/test/stdlib/Rational_test.rb
@@ -72,13 +72,6 @@ def test_ceil
     # a.ceil(ToInt.new) # does not accept to_int
   end
 
-  def test_conj
-    a = 312r
-
-    a.conj
-    a.conjugate
-  end
-
   def test_denominator
     a = 133r