Proofs for Complex Inequalities to Bound a Complex Integral

[Belgium 12]

Hi,

I need two simple proofs of complex inequalities.

1) |1-z|/|z|<2

2)|1+z|/|z|>1/2

Ik need them for a bound of a complex integral.It's not homework

Thank you

 

[Redbelly98]

Both inequalities are false, hence cannot be proven.

Try z=0.1 in (1).
Try z=-1 in (2).

 

[Belgium 12]

Hi,

yes you are right.

But it's my fault,I forgot something.

I have to show this inequalities for z->infinity as a lower and upper bound in a complex

integral.

Sorry