- #1
mynameisfunk
- 125
- 0
given z, w[tex]\in[/tex]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?
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?