Why do we use i to represent phasors and/or vectors?

[friendbobbiny]

Somestimes, vectors (e.g <3,4>) are represented with a real and imaginary component (3 + 4i). When expressing wave phasors as vectors, this is usually the convention.

Insofar as phasors and waves go, what rationale does the convention have? If I had to superimpose two waves together, and perform an assortment of calculations, what role would the "i" term carry?

 

[jedishrfu]

I think the convention came from complex numbers use of i and then when quaternions were the rage the notion of i, j, k was used and later when vectors became more popular the real part was dropped and just the i, j, k remained.