K kspader New member Joined Dec 10, 2013 Messages 1 Dec 10, 2013 #1 Hi, I am having trouble with this problem.. Show that if z lies on the circle |z|=2 then |1/(z^4-4z^2+3)|<(or equal to) 1/3 Should I use the inequality theorem or triangle inequality? or neither...? Thank you!
Hi, I am having trouble with this problem.. Show that if z lies on the circle |z|=2 then |1/(z^4-4z^2+3)|<(or equal to) 1/3 Should I use the inequality theorem or triangle inequality? or neither...? Thank you!
D daon2 Full Member Joined Aug 17, 2011 Messages 999 Dec 11, 2013 #2 kspader said: Hi, I am having trouble with this problem.. Show that if z lies on the circle |z|=2 then |1/(z^4-4z^2+3)|<(or equal to) 1/3 Should I use the inequality theorem or triangle inequality? or neither...? Thank you! Click to expand... \(\displaystyle |z^4-4z^2+3| \ge ||z|^4 -|4z^2-3|| = |16-|4z^2-3||\) but \(\displaystyle |4z^2-3| \le 4|z|^2+3 = 19\) See it now?
kspader said: Hi, I am having trouble with this problem.. Show that if z lies on the circle |z|=2 then |1/(z^4-4z^2+3)|<(or equal to) 1/3 Should I use the inequality theorem or triangle inequality? or neither...? Thank you! Click to expand... \(\displaystyle |z^4-4z^2+3| \ge ||z|^4 -|4z^2-3|| = |16-|4z^2-3||\) but \(\displaystyle |4z^2-3| \le 4|z|^2+3 = 19\) See it now?
