The concept of the modulus of a complex number is due to him. He also gave a beautiful proof (with some gaps) of the fundamental theorem of algebra in 1814.
References (2 books/articles)
A page from a work by Argand:
A translation of a page of Essai sur une manié,re de reprènter les quantitiés imaginaires dans les constructions gèomètriques (1806)
References elsewhere in this archive:
Tell me about Argand's work on abstract linear spaces and on the fundamental theorem of algebra
There is a Dorsa Argand on the moon. You can see a list of lunar features named after mathematicians.
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