diff --git a/tools/chpl-language-server/src/chpl-language-server.py b/tools/chpl-language-server/src/chpl-language-server.py
index aba5c43f14d3..6cdea80286eb 100755
--- a/tools/chpl-language-server/src/chpl-language-server.py
+++ b/tools/chpl-language-server/src/chpl-language-server.py
@@ -142,6 +142,59 @@
 import argparse
 import configargparse
 
+REAL_NUMBERIC = (chapel.RealLiteral, chapel.IntLiteral, chapel.UintLiteral)
+NUMERIC = REAL_NUMBERIC + (chapel.ImagLiteral,)
+
+
+def is_basic_literal_like(node: chapel.AstNode) -> Optional[chapel.Literal]:
+    """
+    Check for "basic" literals: basically, 1, "hello", -42, etc.
+    Returns the "underlying" literal removing surrounding AST (1, "hello", 42).
+    This helps do type comparisons in more complex checks. If the node is
+    not a basic literal, returns None.
+    """
+    if isinstance(node, chapel.Literal):
+        return node
+
+    if (
+        isinstance(node, chapel.OpCall)
+        and node.op() == "-"
+        and node.num_actuals() == 1
+    ):
+        # Do not recurse; do not consider --42 as a basic literal.
+        act = node.actual(0)
+        if isinstance(act, NUMERIC):
+            return act
+
+    return None
+
+
+def is_literal_like(node: chapel.AstNode) -> bool:
+    if is_basic_literal_like(node):
+        return True
+
+    if isinstance(node, chapel.OpCall):
+        # A complex number is far from a literal in the AST; in fact, it
+        # potentially has as many as 4 AST nodes: -1 + 2i has a unary negation,
+        # an addition, and two "pure" literals.
+        op = node.op()
+        if (op == "+" or op == "-") and node.num_actuals() == 2:
+            # The left element can be a 'basic literal-like', like 1 or -42i.
+            # But the right element shouldn't have any operators, otherwise
+            # we'd get somethig that looks like 1 - -42i. So we just
+            # use the right argument directly.
+            left = is_basic_literal_like(node.actual(0))
+            right = node.actual(1)
+
+            real_number = REAL_NUMBERIC
+            imag_number = chapel.ImagLiteral
+            if isinstance(left, real_number) and isinstance(right, imag_number):
+                return True
+            if isinstance(left, imag_number) and isinstance(right, real_number):
+                return True
+
+    return False
+
 
 def decl_kind(decl: chapel.NamedDecl) -> Optional[SymbolKind]:
     if isinstance(decl, chapel.Module) and decl.kind() != "implicit":
@@ -1222,7 +1275,7 @@ def get_call_inlays(
                 # tuples. We don't need hints for those.
                 continue
 
-            if not isinstance(act, chapel.core.Literal):
+            if not is_literal_like(act):
                 # Only show named arguments for literals.
                 continue
 
diff --git a/tools/chpl-language-server/test/call_inlays.py b/tools/chpl-language-server/test/call_inlays.py
index 26e0f1924681..96319914bda9 100644
--- a/tools/chpl-language-server/test/call_inlays.py
+++ b/tools/chpl-language-server/test/call_inlays.py
@@ -75,7 +75,6 @@ async def test_call_inlays(client: LanguageClient):
 
 
 @pytest.mark.asyncio
-@pytest.mark.xfail
 async def test_call_inlays_complex(client: LanguageClient):
     """
     Ensure that call inlays are shown for complex literals in call expressions.
@@ -84,9 +83,44 @@ async def test_call_inlays_complex(client: LanguageClient):
     file = """
            proc foo(a) {}
            foo(3i+10);
+           foo(3i+10.0);
+           foo(3.0i+10.0);
+           foo(3.0i+10);
+           foo(10+3i);
+           foo(10.0+3i);
+           foo(10.0+3.0i);
+           foo(10+3.0i);
+
+           // Not 'literals' in our sense:
+           foo(3i + 4i);
+           foo(1 + 1);
+           foo((-1) - (-i));
            """
 
-    inlays = [(pos((1, 4)), "a = ", None)]
+    inlays = [(pos((i, 4)), "a = ", None) for i in range(1, 9)]
+
+    async with source_file(client, file) as doc:
+        await check_inlay_hints(client, doc, rng((0, 0), endpos(file)), inlays)
+
+
+@pytest.mark.asyncio
+async def test_call_inlays_negative(client: LanguageClient):
+    """
+    Ensure that call inlays are shown for negative literals in call expressions.
+    """
+
+    file = """
+        proc foo(a) {}
+        foo(-42);
+        foo(-42.0);
+        foo(-42i);
+        foo(-42.0i);
+
+        // Not 'literals' in our sense:
+        foo(- -42);
+        """
+
+    inlays = [(pos((i, 4)), "a = ", None) for i in range(1, 5)]
 
     async with source_file(client, file) as doc:
         await check_inlay_hints(client, doc, rng((0, 0), endpos(file)), inlays)