Complex roots

The goal is to completely do without Argand geometry (which is strictly useless in Cartesian planes). Here, we have a curve f(x), which gives us a real root x=1,
since f(x)=(x-1)²(x²+4), but also two complex roots, which are no longer systematically x'=2i and x"=-2i.
This is very strange and worthy of interest.
Thus, f'(x)=x²+4 does not have the same complex roots as f(x)=(x-1)²(x²+4).
This clearly confuses all mathematicians, and even makes them laugh.
And yet it's true.
Just as real roots are unalterable (I can multiply by as many roots as I want, I would always have my first roots continued in the equation), this is no longer true for complex roots. This is very strange.
<http://nemoweb.net/jntp?MgzF4TKP_46j3u1MBdnuxy16Yhg@jntp/Data.Media:1>
<https://www.nemoweb.net/?DataID=MgzF4TKP_46j3u1MBdnuxy16Yhg@jntp>
x'=2i
Yes, but... x"=-0.38829i and not x"=-2i
R.H.