diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 2b4b10c39602a..2805bd9ac2db3 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -424,6 +424,7 @@ I/O
 - Bug in :func:`read_table` and :func:`read_csv` when ``delim_whitespace=True`` and ``sep=default`` (:issue:`36583`)
 - Bug in :meth:`to_json` with ``lines=True`` and ``orient='records'`` the last line of the record is not appended with 'new line character' (:issue:`36888`)
 - Bug in :meth:`read_parquet` with fixed offset timezones. String representation of timezones was not recognized (:issue:`35997`, :issue:`36004`)
+- Bug in output rendering of complex numbers showing too many trailing zeros (:issue:`36799`)
 
 Plotting
 ^^^^^^^^
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 0314bdc4ee8ed..f8b8a2c6b6d10 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -2659,11 +2659,11 @@ def memory_usage(self, index=True, deep=False) -> Series:
         >>> df = pd.DataFrame(data)
         >>> df.head()
            int64  float64            complex128  object  bool
-        0      1      1.0    1.000000+0.000000j       1  True
-        1      1      1.0    1.000000+0.000000j       1  True
-        2      1      1.0    1.000000+0.000000j       1  True
-        3      1      1.0    1.000000+0.000000j       1  True
-        4      1      1.0    1.000000+0.000000j       1  True
+        0      1      1.0              1.0+0.0j       1  True
+        1      1      1.0              1.0+0.0j       1  True
+        2      1      1.0              1.0+0.0j       1  True
+        3      1      1.0              1.0+0.0j       1  True
+        4      1      1.0              1.0+0.0j       1  True
 
         >>> df.memory_usage()
         Index           128
diff --git a/pandas/io/formats/format.py b/pandas/io/formats/format.py
index 3e4780ec21378..f5908cf7ca7bb 100644
--- a/pandas/io/formats/format.py
+++ b/pandas/io/formats/format.py
@@ -1474,9 +1474,9 @@ def format_values_with(float_format):
 
             if self.fixed_width:
                 if is_complex:
-                    result = _trim_zeros_complex(values, self.decimal, na_rep)
+                    result = _trim_zeros_complex(values, self.decimal)
                 else:
-                    result = _trim_zeros_float(values, self.decimal, na_rep)
+                    result = _trim_zeros_float(values, self.decimal)
                 return np.asarray(result, dtype="object")
 
             return values
@@ -1857,29 +1857,42 @@ def just(x):
     return result
 
 
-def _trim_zeros_complex(
-    str_complexes: np.ndarray, decimal: str = ".", na_rep: str = "NaN"
-) -> List[str]:
+def _trim_zeros_complex(str_complexes: np.ndarray, decimal: str = ".") -> List[str]:
     """
     Separates the real and imaginary parts from the complex number, and
     executes the _trim_zeros_float method on each of those.
     """
-    return [
-        "".join(_trim_zeros_float(re.split(r"([j+-])", x), decimal, na_rep))
+    trimmed = [
+        "".join(_trim_zeros_float(re.split(r"([j+-])", x), decimal))
         for x in str_complexes
     ]
 
+    # pad strings to the length of the longest trimmed string for alignment
+    lengths = [len(s) for s in trimmed]
+    max_length = max(lengths)
+    padded = [
+        s[: -((k - 1) // 2 + 1)]  # real part
+        + (max_length - k) // 2 * "0"
+        + s[-((k - 1) // 2 + 1) : -((k - 1) // 2)]  # + / -
+        + s[-((k - 1) // 2) : -1]  # imaginary part
+        + (max_length - k) // 2 * "0"
+        + s[-1]
+        for s, k in zip(trimmed, lengths)
+    ]
+    return padded
+
 
 def _trim_zeros_float(
-    str_floats: Union[np.ndarray, List[str]], decimal: str = ".", na_rep: str = "NaN"
+    str_floats: Union[np.ndarray, List[str]], decimal: str = "."
 ) -> List[str]:
     """
     Trims zeros, leaving just one before the decimal points if need be.
     """
     trimmed = str_floats
+    number_regex = re.compile(fr"\s*[\+-]?[0-9]+(\{decimal}[0-9]*)?")
 
     def _is_number(x):
-        return x != na_rep and not x.endswith("inf")
+        return re.match(number_regex, x) is not None
 
     def _cond(values):
         finite = [x for x in values if _is_number(x)]
diff --git a/pandas/tests/io/formats/test_format.py b/pandas/tests/io/formats/test_format.py
index 68f5386fff7be..b30ceed23b02e 100644
--- a/pandas/tests/io/formats/test_format.py
+++ b/pandas/tests/io/formats/test_format.py
@@ -3432,3 +3432,10 @@ def test_format_remove_leading_space_dataframe(input_array, expected):
     # GH: 24980
     df = pd.DataFrame(input_array).to_string(index=False)
     assert df == expected
+
+
+def test_to_string_complex_number_trims_zeros():
+    s = pd.Series([1.000000 + 1.000000j, 1.0 + 1.0j, 1.05 + 1.0j])
+    result = s.to_string()
+    expected = "0    1.00+1.00j\n1    1.00+1.00j\n2    1.05+1.00j"
+    assert result == expected