This is obviously not a completely serious question but it is definitely looks like a question someone might ask when learning about complex numbers for the first time.

The answer is completely historical in nature. Imaginary numbers began as being interpreted as the square root of -1 for the purposes of solving polynomial equations (hence the name.) Later, their field structure and their interpretation as vectors-with-multiplication became their primary use but the name remained.

Mathematicians don't really use "vectors" in the traditional sense like in physics but deal with abstract vector spaces where a "vector" is simply a member of a "vector space" which is "a set of things with addition and scalar multiplication and a few other nice properties".

However, if something needs to be done with vectors in a plane, complex numbers are extremely useful because scaling and rotation can be represented as multiplication. Therefore natural operations in the complex numbers often correspond to natural operations in whatever you are trying to study with complex numbers.

> Mathematicians don't really use "vectors" in the traditional sense like in physics but deal with abstract vector spaces

This is not at all true in general: many mathematicians use non-abstract vectors too. My (maths) PhD, for example, uses vectors throughout but doesn't mention vector spaces once.

I wonder, how many people downvoted this without following the link to the comic? It's relevant, intelligent, and funny.