sentence1: How do I show that -LSB- math -RSB- | \ alpha | \ leq max -LSB- / math -RSB- -LCB- -LSB- math -RSB- 1 , \ sum _ -LCB- i = 0 -RCB- ^ -LCB- n-1 -RCB- | a_i | -LSB- / math -RSB- -RCB- where -LSB- math -RSB- \ alpha -LSB- / math -RSB- is zero of -LSB- math -RSB- p -LRB- x -RRB- = \ sum _ -LCB- i = 0 -RCB- ^ -LCB- n -RCB- a_i x ^ i , -LSB- / math -RSB- where -LSB- math -RSB- a_i -LSB- / math -RSB- may be complex and -LSB- math -RSB- a_n = 1 -LSB- / math -RSB- ?
sentence2: If -LSB- math -RSB- \ alpha -LSB- / math -RSB- is a root of -LSB- math -RSB- p -LRB- x -RRB- = x ^ n + a _ -LCB- n-1 -RCB- x ^ -LCB- n-1 -RCB- + ... + a_0 -LSB- / math -RSB- where -LSB- math -RSB- a_i -LSB- / math -RSB- may be complex , how do I prove that -LSB- math -RSB- | \ alpha | \ leq \ max \ -LCB- 1 , | a_0 | + | a_1 | + ... + | a _ -LCB- n-1 -RCB- | \ -RCB- -LSB- / math -RSB- ?