Is it possible for a degree-5 polynomial over the complex numbers to have 1 as a root of multiplicity 1, i as a root of multiplicity 2, and no other roots?
I am trying to find an example where this is true. What I've come up with is
$(x-1)(x-i)^2$ but this has only degree 3. I cannot think of any examples over the complex numbers that make this statement true. I am thinking it is not a true statement. Any feedback would be appreciated.