Hey all. I am giving Panhellenic exams this year, and part of my preparation comes from solving previous' years questions. This problem was a complex number based one, in the 2013 Panhellenic exams. It goes as follows: Consider 3 complex numbers, α0,α1 and α2 which belong in the line given by the following equation: (α-2)(α'-2)+|α-2|=2 , where α∈ℂ and α' is α's conjugate If complex number v satisfies the following expression: v3+α2v2+α1v+α0=0 , Prove that: |v|<4 It is said that it was the hardest complex number problem they ever put in the exam, and it was totally against exam "spirit". By the way the exams are done in the last year of Senior High School. I really want to hear your opinions on the matter. Thanks for reading. Michael. EDIT: I apologize if this is the wrong forum for this question. I've been a member for quite a while now but i haven't visited in many years. I didn't post this problem here to get it solved. I just wanted people to discuss it and give their thoughts about the exams. If i broke any guidelines please move my thread, i didn't mean to cause harm.