The conversation between human and AI assistant.
How do I show that [math]|\alpha| \leq max[/math] {[math]1, \sum_{i=0}^{n-1} |a_i|[/math]} where [math]\alpha [/math] is zero of [math]p(x)=\sum_{i=0}^{n} a_i x^i,[/math] where [math]a_i[/math] may be complex and [math]a_n =1[/math]?
I need to show that [math]|\alpha| \leq max[/math] {[math]1, \sum_{i=0}^{n-1} |a_i|[/math]} where [math]\alpha [/math] is zero of [math]p(x)=\sum_{i=0}^{n} a_i x^i,[/math] where [math]a_i[/math] may be complex and [math]a_n =1[/math].
To start, let me clarify the variables you mentioned. [math]\alpha[/math] is a zero of polynomial [math]p(x)[/math], whose coefficient of degree [math]n[/math] is [math]a_n = 1[/math], and [math]a_i[/math] can be complex for [math]i \in \{0,1,..., n-1\}[/math]. Is that correct?