When do |z+w| and |z-w| equal for complex numbers?

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mynameisfunk
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OK, in my book we have an inequality ||z|-|w||[tex]\leq[/tex]|z+w|[tex]\leq[/tex]|z|+|w| then from here it simply states, "Replacing w by -w here shows that ||z|-|w||[tex]\leq[/tex]|z-w|[tex]\leq[/tex]|z|+|w|.

How do we know that?
is |z+w|=|z-w|?? Note that z and w are complex numbers.
 

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No, |z+w| is NOT equal to |z-w|. Your first inequality is true for all w. Therefore it also must be true for -w. Substitute '-w' everywhere you see 'w' in the first inequality.
 
Dick said:
No, |z+w| is NOT equal to |z-w|. Your first inequality is true for all w. Therefore it also must be true for -w. Substitute '-w' everywhere you see 'w' in the first inequality.

Thanks a lot Dick, again. You rock