I’m aware my son is an outlier, but I’m rather proud of his working out the square root(s) of i without even having algebra yet (he’s in fifth grade). Last year I taught him how to solve simple linear equations (ax + b = c) and expanded that to ax + b = cx + d, but he’s been mostly an autodidact with his advanced math (consulting youtube videos and books from the library).
But yeah, there seems not to be a lot of assumption of familiarity with complex numbers beyond the basics of their existence and maybe some simple arithmetic on numbers in the form a + bi which other than i² = −1 is just following the usual rules for polynomial arithmetic. I was surprised at how much basic content on complex numbers was included in the first chapter of my graduate text on complex analysis.
In fact, it is practically assumed that elementary algebra students have not worked with complex numbers to the extent necessary to understand complex exponentials, due to the fact that complex exponentials are not algebraic.