Add tolerance to complex numbers

changelog/6057.feature.rst

@@ -0,0 +1,3 @@
+Add tolerances to complex values when printing ``pytest.approx``.
+
+For example, ``repr(pytest.approx(3+4j))`` returns ``(3+4j) ± 5e-06 ∠ ±180°``. This is polar notation indicating a circle around the expected value, with a radius of 5e-06. For ``approx`` comparisons to return ``True``, the actual value should fall within this circle.

src/_pytest/python_api.py

@@ -223,26 +223,24 @@ class ApproxScalar(ApproxBase):
     def __repr__(self):
         """
         Return a string communicating both the expected value and the tolerance
-        for the comparison being made, e.g. '1.0 +- 1e-6'.  Use the unicode
-        plus/minus symbol if this is python3 (it's too hard to get right for
-        python2).
+        for the comparison being made, e.g. '1.0 ± 1e-6', '(3+4j) ± 5e-6 ∠ ±180°'.
         """
-        if isinstance(self.expected, complex):
-            return str(self.expected)
 
         # Infinities aren't compared using tolerances, so don't show a
         # tolerance.
-        if math.isinf(self.expected):
+        if math.isinf(abs(self.expected)):
             return str(self.expected)
 
         # If a sensible tolerance can't be calculated, self.tolerance will
         # raise a ValueError.  In this case, display '???'.
         try:
             vetted_tolerance = "{:.1e}".format(self.tolerance)
+            if isinstance(self.expected, complex) and not math.isinf(self.tolerance):
+                vetted_tolerance += " ∠ ±180°"
         except ValueError:
             vetted_tolerance = "???"
 
-        return "{} \u00b1 {}".format(self.expected, vetted_tolerance)
+        return "{} ± {}".format(self.expected, vetted_tolerance)
 
     def __eq__(self, actual):
         """

testing/python/approx.py

@@ -46,7 +46,6 @@ class TestApprox:
         assert repr(approx(1.0, rel=inf)) == "1.0 {pm} {infr}".format(
             pm=plus_minus, infr=infr
         )
-        assert repr(approx(1.0j, rel=inf)) == "1j"
 
         # Dictionaries aren't ordered, so we need to check both orders.
         assert repr(approx({"a": 1.0, "b": 2.0})) in (
@@ -58,6 +57,21 @@ class TestApprox:
             ),
         )
 
+    def test_repr_complex_numbers(self):
+        assert repr(approx(inf + 1j)) == "(inf+1j)"
+        assert repr(approx(1.0j, rel=inf)) == "1j ± inf"
+
+        # can't compute a sensible tolerance
+        assert repr(approx(nan + 1j)) == "(nan+1j) ± ???"
+
+        assert repr(approx(1.0j)) == "1j ± 1.0e-06 ∠ ±180°"
+
+        # relative tolerance is scaled to |3+4j| = 5
+        assert repr(approx(3 + 4 * 1j)) == "(3+4j) ± 5.0e-06 ∠ ±180°"
+
+        # absolute tolerance is not scaled
+        assert repr(approx(3.3 + 4.4 * 1j, abs=0.02)) == "(3.3+4.4j) ± 2.0e-02 ∠ ±180°"
+
     @pytest.mark.parametrize(
         "value, repr_string",
         [