# Complex Inequality

1. May 9, 2005

### eckiller

Hello,

I have the inequality

t > (1/2) + a / |w|^2

where w is a complex number, w = a + bi. So the a in the inequality is the
real part.

So I need to find t such that all w are in a sector around the negative real
axis. Note t in [0, 1].

I am having trouble figuring out the condition to impose.

For example, before I wanted to find t such that the entire negative half of the complex plane satisfied the above inequality. t > 1/2 clearly satisfied this. Now I want to find t such that a sector around the negative real
axis satisfies the above inequality.