given z, w[tex]\in[/tex](adsbygoogle = window.adsbygoogle || []).push({}); C, and |z|=([conjugate of z]z)^{1/2}, prove ||z|-|w|| [tex]\leq[/tex] |z-w| [tex]\leq[/tex] |z|+|w|

I squared all three terms and ended up with :

-2|z||w| [tex]\leq[/tex] |-2zw| [tex]\leq[/tex] 2|z||w|

I know this leaves the right 2 equal to each other but i figured if i show that since there exists a z[tex]\geq[/tex]w[tex]\geq[/tex]0, then |z-w| > |z|+|w| would be impossible.

Can someone tell me if they think I screwed up or I am not done?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Triangle inequality w/ Complex Numbers

**Physics Forums | Science Articles, Homework Help, Discussion**