# 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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– 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.