# Very clever complex inequality.

1. Jun 28, 2008

### mathwizarddud

Prove that for every complex number z it happens that:

$$|z+10|+|z+11|+|z+19| \le |z+8|+|z+12|+|z+20|$$

2. Jun 28, 2008

### alyscia

let z = a+ bi and physically evaluate the modulus.

Is this some homework question? I am not sure why this is in the analysis section.