# Problem of modulus of complex numbers

If $a$ is a complex number $a\neq 0$. Under that conditions $|a|\leq |a+z|$ with $z$ complex number?

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Are you searching for a set of complex numbers which satisfy your conditions? Something like $\{z \in \mathbb{C} | |a| \le |a+z|\}$ ? Also, you should work on your accept rate. –  Stefan Oct 2 '12 at 1:04
Why the 0% accept rate ? –  Belgi Oct 2 '12 at 1:04
Belgi sorry what is the accept rate? –  Roiner Segura Cubero Oct 2 '12 at 1:10
–  user39572 Oct 2 '12 at 1:16
That condition is equivalent to $d(a,0) \le d(a,-z)$. Time to draw a picture and see what is happening.