The proper style for an argumentative essay is

academic.

friendly.

informal.

personal.

The correct answer is academic.

Argumentative essays require you to use extensive research so that you can make your arguments stronger. You will usually present the argument you are fighting against, and the arguments that you want to support, and therefore you need to convince the reader to believe you. You will do that by using academic style and vocabulary, rather than friendly, informal, or personal.