± is actually a standard character and you can type it in by using Alt+0177. As the Character Map showed, the hexadecimal code is B1, and so with the Quick Unicode utility you can type Alt . * 1 and get the same character.
Be aware, however, that character codes are just character codes with no font attached. For example, if you type the hexadecimal code 61 in the Symbol font, you will see a Greek letter alpha ('α'); but in any font other than Symbol it will appear as a lower-case Latin letter 'a'. You have a choice: you can find the correct Unicode code for the character you want (alpha is U+03B1, or Alt . 3 * 1 with Quick Unicode), or you can tell your application that the character you typed is in the Symbol font. How you do that depends entirely on the application you are using.