Complex Analysis

[kspader]

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!

 

[daon2]

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!

\(\displaystyle |z^4-4z^2+3| \ge ||z|^4 -|4z^2-3|| = |16-|4z^2-3||\)

but

\(\displaystyle |4z^2-3| \le 4|z|^2+3 = 19\)

See it now?