You input only 2D-elements, ordered pairs of real numbers-thus vectors of the R2.
The rules of their computation were invented by Bombelli.He used a form of notation
similar to 3+i*4, Hamilton notated (3,4) and Cayley invented the matrices.
For the first time they are combined in this calculator: input i* (3,4),
the result is a rotation to the left by 90 degrees of the vector (3,4),so i*(3,4)=(-4,3).

Are these complex numbers?Is"i"imaginary?Is Bombelli (R2,+,*) isomorph to (C,+,*)?
It's a "sensitive question" for some - so, i leave the answer to them. And,
i'm afraid (for them), a computer won't notice a difference.The geometrical representation
is since Wessel any ordinary plane, the vectors in the modern form of arrows - and so:
forget an imaginary axis, a Gauss-plane, a complex plane, an Argand diagramm and C.