Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 - Kaoutar Lamrini Uahabi; Mohammed Zaoui (International Journal of Mathematics and Mathematical Sciences)
We deal with the family B(n,k,r) of trinomial arcs defined as the set of roots of the trinomial equation zn=αzk+(1−α), where z=ρeiθ is a complex number, n and k are two integers such that 0<k<n, and α is a real number between 0 and 1. These arcs B(n,k,r) are continuous arcs inside the unit disk, expressed in polar coordinates (ρ,θ). The question is to prove that ρ(θ) is a decreasing function, for each trinomial arc B(n,k,r).