The polynomial-power conjecture on Taylor-polynomial intersection roots

Suppose that $f(z)=z^n$, where $n\in\mathbb{N}$ and $n\geq r+1$, and let $P_c$ denote the Taylor polynomial of $f$ of order $r$ at $x=c$. Polynomial-power conjecture. Every pair of complex conjugate roots of $P_b-P_a$ has real part lying between $a$ and $b$. This is a more specific root-location claim for Taylor polynomials of the monomial $z^n$. The supplied status evidence states that Conjecture CJ2 does not hold in general for $f(z)=z^{-n}$, with $n\in\mathbb{N}$, so the candidate is marked refuted.