diff --git a/pyquil/quilatom.py b/pyquil/quilatom.py
index 8028068e6..fd7b7f026 100644
--- a/pyquil/quilatom.py
+++ b/pyquil/quilatom.py
@@ -419,13 +419,15 @@ def format_parameter(element: ParameterDesignator) -> str:
             out += repr(r)
 
         if i == 1:
-            if not np.isclose(r, 0, atol=1e-14):
-                raise ValueError(f"Invalid complex number: {element}")
-            out = "i"
+            if np.isclose(r, 0, atol=1e-14):
+                out = "i"
+            else:
+                out += "+i"
         elif i == -1:
-            if not np.isclose(r, 0, atol=1e-14):
-                raise ValueError(f"Invalid complex number: {element}")
-            out = "-i"
+            if np.isclose(r, 0, atol=1e-14):
+                out = "-i"
+            else:
+                out += "-i"
         elif i < 0:
             out += repr(i) + "i"
         elif r != 0:
diff --git a/test/unit/test_parameters.py b/test/unit/test_parameters.py
index 355856b77..827a0679a 100644
--- a/test/unit/test_parameters.py
+++ b/test/unit/test_parameters.py
@@ -24,6 +24,9 @@ def test_format_parameter():
         (-1j, "-i"),
         (1e-15 + 1j, "i"),
         (1e-15 - 1j, "-i"),
+        (2 + 1j, "2.0+i"),
+        (2 - 1j, "2.0-i"),
+        (-3 + 1j, "-3.0+i"),
     ]
 
     for test_case in test_cases: