Hi,

I need two proofs for complex inequalities.

1) |1-z|/z <2 or equal.

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

thanks

Printable View

- Nov 12th 2009, 10:37 AMGilbertcomplex variables
Hi,

I need two proofs for complex inequalities.

1) |1-z|/z <2 or equal.

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

thanks - Nov 12th 2009, 11:06 AMtonio

Proofs...of what? I think you have to describe the set of points on the (complex) plane that fulfill the given inequalities, so put and (I think an absolute value (modulus) is lacking in the denominator of the first one):

And we got a nice circle with center__ and radius__ . Now you try the second one.

Tonio - Nov 12th 2009, 12:09 PMGilbertcomplex variables
Hi,

maybe not a proof,but I have to show these inequalities.I need them for

the bound of a complex integral.

I taught something like that

|z+1|>|z-1|=1/2|z|+|1/2|z|-1|>1/2|z| but I'm not sure it's correct.

Tanks - Nov 12th 2009, 12:21 PMtonio
- Nov 12th 2009, 12:56 PMGilbertComplex variables
Hi,

yes you are right,but it's my fault.I have to show this inequalities for

z->infinity

as an upper bound and lower bound.

Sorry

Thanks