Erase from your mind that 'complex' numbers have anything to do with the square root of $-1$. Instead ask yourself if this is feasible:
Intelligent life in a distant part of the universe developed in a completely different way than we did. They often say
God made the polygons, all else is the work of ___.
This species made great strides in algebra at a very early stage. They built up considerable 'mathematical potential energy' in their ancient history.
In a short span of time, they went from the polygons to the circle, and then realized that there was a natural covering map of the 1-dim number line onto the circle group. For them, the circle group of rotations iswas just as useful as the number line. Very quickly in there technical advancement
As they worked with 2-dim space, one of their greatest minds realized that they could create a useful number system that contained boththe most natural way to extend multiplication from the circle and number lines to all the line.
They were happy with this new constructionpoints in the plane was to multiply number lengths and add their angles (dilation/rotation). They found that someIt was a flash of intuition and insight, but the theory details gave then a tremendous technological advancement; many math problems they worked on had a new feel to them (for example, sincethey found that every polynomial could now be completely factored).
As they advanced into quantum mechanics, they developed, what we humans call, the Schrödinger equation,
$i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf {r} ,t)={\hat {H}}\Psi (\mathbf {r} ,t)$
Of course they did not express it as we do, and they were really surprised when they learned that $i$ meant "imaginary number" to so many people on earth. They were even more surprised to learn what percentage of people even knew what it stood for.