Need help with complex number inequalities?

[3102]

Hi!

At university I have got a problem set with lots of inequalities. Unfortunately there are no explanations given how to do them. In Highschool we only did very easy inequalities.
Therefore I am looking for a resource for inequalities. Especially for more difficult inequalities like $$ 1 \leq z \overline {z} \leq 4 , |\Im(z)|<\Re (z),$$ where $z$ is a complex number.

I would be glad at any recommendations.

 

[jedishrfu]

what course are you taking where you find these inequalities? Complex analysis?

 

[fourier jr]

that looks like the kinds of problems you would do when first learning about complex numbers. the first one involves an identity with the modulus, and the second one looks almost self-explatory. just try a few examples where it's true & I think it will become clear. I don't think you need a whole book on inequalities if you're doing complex analysis & those are the problems you have. just apply what you know about complex numbers to find the regions where they're true.