diff --git a/README.md b/README.md
index a5a227c..7c76fd7 100644
--- a/README.md
+++ b/README.md
@@ -44,6 +44,21 @@ iex> Complex.new(0, 1)
 %Complex{im: 1.0, re: 0.0}
 ```
 
+### Sigil
+
+`import Complex, only: :sigils` gives you the `~COMPLEX` and `~POLAR` sigils.
+The two numbers are separated by whitespace; `~COMPLEX` mirrors Common
+Lisp's `#c(re im)` reader syntax. They are meant for literals; for
+variables use `Complex.new/2` and `Complex.from_polar/2`:
+
+```elixir
+iex> ~COMPLEX(3 4)
+%Complex{im: 4, re: 3}
+
+iex> ~POLAR(2 1.57)
+Complex.from_polar(2, 1.57)
+```
+
 ## License
 
    Copyright 2015 Thomas Krauss
diff --git a/lib/complex.ex b/lib/complex.ex
index 1b79384..ef8f8ff 100644
--- a/lib/complex.ex
+++ b/lib/complex.ex
@@ -288,6 +288,69 @@ defmodule Complex do
     end
   end
 
+  @doc ~S"""
+  Handles the sigil `~COMPLEX` for complex numbers in cartesian form.
+
+  The real and imaginary parts are separated by whitespace, mirroring
+  Common Lisp's `#c(re im)` reader syntax. Uppercase sigils do not
+  interpolate, so for variables use `new/2`.
+
+  Use `import Complex, only: :sigils` to make it available.
+
+  ### See also
+
+  `new/2`, `sigil_POLAR/2`
+
+  ### Examples
+
+      import Complex, only: :sigils
+
+      ~COMPLEX(3 4)
+      #=> %Complex{re: 3, im: 4}
+  """
+  @spec sigil_COMPLEX(String.t(), []) :: t
+  def sigil_COMPLEX(string, []) do
+    [re, im] = sigil_numbers(string)
+    new(re, im)
+  end
+
+  @doc ~S"""
+  Handles the sigil `~POLAR` for complex numbers in polar form.
+
+  The magnitude and the angle (in radians) are separated by whitespace.
+  Uppercase sigils do not interpolate, so for variables use `from_polar/2`.
+
+  Use `import Complex, only: :sigils` to make it available.
+
+  ### See also
+
+  `from_polar/2`, `sigil_COMPLEX/2`
+
+  ### Examples
+
+      import Complex, only: :sigils
+
+      ~POLAR(2 1.57)
+      #=> Complex.from_polar(2, 1.57)
+  """
+  @spec sigil_POLAR(String.t(), []) :: t
+  def sigil_POLAR(string, []) do
+    [r, phi] = sigil_numbers(string)
+    from_polar(r, phi)
+  end
+
+  defp sigil_numbers(string), do: string |> String.split() |> Enum.map(&sigil_number/1)
+
+  defp sigil_number(str) do
+    with :error <- exact_parse(Integer.parse(str)),
+         :error <- exact_parse(Float.parse(str)) do
+      raise ArgumentError, "invalid number in complex sigil: #{inspect(str)}"
+    end
+  end
+
+  defp exact_parse({n, ""}), do: n
+  defp exact_parse(_), do: :error
+
   @doc """
   Returns the phase angle of the supplied complex, in radians.
 
diff --git a/test/complex/sigils_test.exs b/test/complex/sigils_test.exs
new file mode 100644
index 0000000..3668acb
--- /dev/null
+++ b/test/complex/sigils_test.exs
@@ -0,0 +1,43 @@
+defmodule Complex.SigilsTest do
+  use ExUnit.Case, async: true
+
+  import Complex, only: :sigils
+
+  test "~COMPLEX builds a complex number from integers" do
+    assert ~COMPLEX(3 4) == Complex.new(3, 4)
+  end
+
+  test "~COMPLEX keeps integers and floats as written" do
+    assert ~COMPLEX(3 -4.5) === Complex.new(3, -4.5)
+  end
+
+  test "extra whitespace is ignored" do
+    assert ~COMPLEX(  3    4  ) == Complex.new(3, 4)
+  end
+
+  test "~POLAR builds a complex number from magnitude and angle" do
+    assert ~POLAR(2 1.57) == Complex.from_polar(2, 1.57)
+  end
+
+  test "it raises on an invalid number" do
+    assert_raise ArgumentError, ~r/invalid number/, fn ->
+      Complex.sigil_COMPLEX("3 x", [])
+    end
+
+    assert_raise ArgumentError, ~r/invalid number/, fn ->
+      Complex.sigil_POLAR("3 x", [])
+    end
+  end
+
+  test "it raises when there are not exactly two numbers" do
+    assert_raise MatchError, fn -> Complex.sigil_COMPLEX("3", []) end
+    assert_raise MatchError, fn -> Complex.sigil_POLAR("1 2 3", []) end
+  end
+
+  test "it raises on modifiers" do
+    # apply/3 keeps the compiler's type checker from flagging the call,
+    # which can never match the `[]` modifiers clause
+    assert_raise FunctionClauseError, fn -> apply(Complex, :sigil_COMPLEX, ["3 4", ~c"x"]) end
+    assert_raise FunctionClauseError, fn -> apply(Complex, :sigil_POLAR, ["3 4", ~c"p"]) end
+  end
+end