diff --git a/changelog/6057.feature.rst b/changelog/6057.feature.rst
new file mode 100644
index 000000000..b7334e7fe
--- /dev/null
+++ b/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.
diff --git a/src/_pytest/python_api.py b/src/_pytest/python_api.py
index f03d45ab7..52a91a905 100644
--- a/src/_pytest/python_api.py
+++ b/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):
+        # tolerance. Need to call abs to handle complex numbers, e.g. (inf + 1j)
+        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):
         """
diff --git a/testing/python/approx.py b/testing/python/approx.py
index 0575557ae..60fde151a 100644
--- a/testing/python/approx.py
+++ b/testing/python/approx.py
@@ -24,55 +24,50 @@ class MyDocTestRunner(doctest.DocTestRunner):
 
 
 class TestApprox:
-    @pytest.fixture
-    def plus_minus(self):
-        return "\u00b1"
-
-    def test_repr_string(self, plus_minus):
-        tol1, tol2, infr = "1.0e-06", "2.0e-06", "inf"
-        assert repr(approx(1.0)) == "1.0 {pm} {tol1}".format(pm=plus_minus, tol1=tol1)
-        assert repr(
-            approx([1.0, 2.0])
-        ) == "approx([1.0 {pm} {tol1}, 2.0 {pm} {tol2}])".format(
-            pm=plus_minus, tol1=tol1, tol2=tol2
-        )
-        assert repr(
-            approx((1.0, 2.0))
-        ) == "approx((1.0 {pm} {tol1}, 2.0 {pm} {tol2}))".format(
-            pm=plus_minus, tol1=tol1, tol2=tol2
-        )
+    def test_repr_string(self):
+        assert repr(approx(1.0)) == "1.0 ± 1.0e-06"
+        assert repr(approx([1.0, 2.0])) == "approx([1.0 ± 1.0e-06, 2.0 ± 2.0e-06])"
+        assert repr(approx((1.0, 2.0))) == "approx((1.0 ± 1.0e-06, 2.0 ± 2.0e-06))"
         assert repr(approx(inf)) == "inf"
-        assert repr(approx(1.0, rel=nan)) == "1.0 {pm} ???".format(pm=plus_minus)
-        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"
+        assert repr(approx(1.0, rel=nan)) == "1.0 ± ???"
+        assert repr(approx(1.0, rel=inf)) == "1.0 ± inf"
 
         # Dictionaries aren't ordered, so we need to check both orders.
         assert repr(approx({"a": 1.0, "b": 2.0})) in (
-            "approx({{'a': 1.0 {pm} {tol1}, 'b': 2.0 {pm} {tol2}}})".format(
-                pm=plus_minus, tol1=tol1, tol2=tol2
-            ),
-            "approx({{'b': 2.0 {pm} {tol2}, 'a': 1.0 {pm} {tol1}}})".format(
-                pm=plus_minus, tol1=tol1, tol2=tol2
-            ),
+            "approx({'a': 1.0 ± 1.0e-06, 'b': 2.0 ± 2.0e-06})",
+            "approx({'b': 2.0 ± 2.0e-06, 'a': 1.0 ± 1.0e-06})",
         )
 
+    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",
+        "value, expected_repr_string",
         [
-            (5.0, "approx(5.0 {pm} 5.0e-06)"),
-            ([5.0], "approx([5.0 {pm} 5.0e-06])"),
-            ([[5.0]], "approx([[5.0 {pm} 5.0e-06]])"),
-            ([[5.0, 6.0]], "approx([[5.0 {pm} 5.0e-06, 6.0 {pm} 6.0e-06]])"),
-            ([[5.0], [6.0]], "approx([[5.0 {pm} 5.0e-06], [6.0 {pm} 6.0e-06]])"),
+            (5.0, "approx(5.0 ± 5.0e-06)"),
+            ([5.0], "approx([5.0 ± 5.0e-06])"),
+            ([[5.0]], "approx([[5.0 ± 5.0e-06]])"),
+            ([[5.0, 6.0]], "approx([[5.0 ± 5.0e-06, 6.0 ± 6.0e-06]])"),
+            ([[5.0], [6.0]], "approx([[5.0 ± 5.0e-06], [6.0 ± 6.0e-06]])"),
         ],
     )
-    def test_repr_nd_array(self, plus_minus, value, repr_string):
+    def test_repr_nd_array(self, value, expected_repr_string):
         """Make sure that arrays of all different dimensions are repr'd correctly."""
         np = pytest.importorskip("numpy")
         np_array = np.array(value)
-        assert repr(approx(np_array)) == repr_string.format(pm=plus_minus)
+        assert repr(approx(np_array)) == expected_repr_string
 
     def test_operator_overloading(self):
         assert 1 == approx(1, rel=1e-6, abs=1e-12)