For complex number z, how to show that max_{|z|<=1} |az^{n}+b|=|a|+|b| where a, b are real number?
Follow Math Help Forum on Facebook and Google+
Originally Posted by shyuan For complex number z, how to show that max_{|z|<=1} |az^{n}+b|=|a|+|b| where a, b are real number? Use the triangle inequality: . So Therefore .
but this only prove that |a|+|b| is on eof the upper bound, not necessary to be the maximum value right?
Originally Posted by shyuan but this only prove that |a|+|b| is on eof the upper bound, not necessary to be the maximum value right? If it's the least upper bound (which it is) and a possible value (which it also is), then it is the maximum value.
thx for ur help bt cn i ask, hw to confirm that it is already the least upper bound?
Originally Posted by shyuan this only prove that |a|+|b| is on eof the upper bound, not necessary to be the maximum value right? Given a, b and n, try to find a z with |z| = 1 such that |ax^n + b| = |a| + |b|.
Thank you very much. I solved my problem with the helps from you guys. Thanks.
View Tag Cloud