diff --git a/crates/literal/src/complex.rs b/crates/literal/src/complex.rs
index bbfc88cb3..20d694f8e 100644
--- a/crates/literal/src/complex.rs
+++ b/crates/literal/src/complex.rs
@@ -70,6 +70,14 @@ pub fn parse_str(s: &str) -> Option<(f64, f64)> {
         Some(s) => s.strip_suffix(')')?.trim(),
     };
 
+    // Whitespace is only allowed around the whole string and the optional
+    // parentheses, never inside the numeric token. Reject it here so that
+    // `float::parse_str` (which tolerates surrounding whitespace on a part)
+    // does not let e.g. "1 +2j" through.
+    if s.contains(char::is_whitespace) {
+        return None;
+    }
+
     let value = match s.strip_suffix(|c| c == 'j' || c == 'J') {
         None => (float::parse_str(s)?, 0.0),
         Some(mut s) => {
@@ -96,3 +104,39 @@ pub fn parse_str(s: &str) -> Option<(f64, f64)> {
     };
     Some(value)
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn parse_rejects_internal_whitespace() {
+        // Whitespace inside the numeric token is invalid, even where a bare
+        // `float::parse_str` on a fragment would tolerate it.
+        for s in [
+            "1 +2j", "1 2j", "1 +2 j", "+ 1j", "1.5 j", "(1 +2j)", "2 -3j",
+        ] {
+            assert_eq!(parse_str(s), None, "{s:?} must not parse");
+        }
+    }
+
+    #[test]
+    fn parse_allows_surrounding_and_paren_whitespace() {
+        for s in ["  1+2j  ", " (1+2j) ", "( 1+2j )"] {
+            assert_eq!(parse_str(s), Some((1.0, 2.0)), "{s:?}");
+        }
+    }
+
+    #[test]
+    fn parse_basic() {
+        assert_eq!(parse_str("1"), Some((1.0, 0.0)));
+        assert_eq!(parse_str("1j"), Some((0.0, 1.0)));
+        assert_eq!(parse_str("j"), Some((0.0, 1.0)));
+        assert_eq!(parse_str("-j"), Some((0.0, -1.0)));
+        assert_eq!(parse_str("1+2j"), Some((1.0, 2.0)));
+        assert_eq!(parse_str("1e5j"), Some((0.0, 1e5)));
+        assert_eq!(parse_str("1_000"), Some((1000.0, 0.0)));
+        assert_eq!(parse_str(""), None);
+        assert_eq!(parse_str("abc"), None);
+    }
+}
diff --git a/extra_tests/snippets/builtin_complex.py b/extra_tests/snippets/builtin_complex.py
index 136f26ef0..55ab38c88 100644
--- a/extra_tests/snippets/builtin_complex.py
+++ b/extra_tests/snippets/builtin_complex.py
@@ -168,6 +168,15 @@ assert complex("-2j") == -2j
 assert_raises(TypeError, lambda: complex("5+2j", 1))
 assert_raises(ValueError, lambda: complex("abc"))
 
+# whitespace is allowed around the string and the optional parentheses,
+# but not inside the numeric token
+assert complex("  1+2j  ") == 1 + 2j
+assert complex("(1+2j)") == 1 + 2j
+assert complex(" ( 1+2j ) ") == 1 + 2j
+assert_raises(ValueError, lambda: complex("1 +2j"))
+assert_raises(ValueError, lambda: complex("1+ 2j"))
+assert_raises(ValueError, lambda: complex("1 + 2j"))
+
 assert complex("1+10j") == 1 + 10j
 assert complex(10) == 10 + 0j
 assert complex(10.0) == 10 + 0j