# Homework Help: Triangle inequality in Rubins book

1. Sep 9, 2010

### mynameisfunk

My problem states:
Given z, w$$\in$$C, prove: ||z|-|w||$$\leq$$|z-w|$$\leq$$|z|+|w|.

Now, I am confused because, isn't it true that ||z|-|w||=|z-w| ? I am using Rudin's book which gives |z|=([z's conjugate]z)1/2

2. Sep 9, 2010

### xepma

Take z =-2 and w = 2. Does ||z|-|w||=|z-w| still hold?

3. Sep 9, 2010

### mynameisfunk

Ah. Thank you. Is it correct from the definition of |z| to think of it as a length? My gf is taking a complex variables class and she had told me that |z|= the length of z, but rudin's book gave the definition above, so i didn't know how to think about it.