If x, y are complex, prove that

||x| - |y|| < = |x - y|

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- Jun 11th 2006, 04:49 PMNichelle14Proof
If x, y are complex, prove that

||x| - |y|| < = |x - y| - Jun 14th 2006, 12:34 AMnath_quamComplex signs??
absolute value or modulus signs

- Jun 14th 2006, 07:53 AMTD!
I'll be using the triangle inequality, which also holds for complex numbers:

We can write:

Doing the same in reverse (changing roles of y and x), yields:

The result follows immediately now. - Jun 14th 2006, 03:28 PMThePerfectHacker
For all, ,

Thus,

Thus,

Thus, adding same quality to both sides,

Thus,

Thus, take square root (note terms are non-negative),

--> Cauchy-Swartchz

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Assume, then,

Thus,

Thus, adding same quality to both sides,

Thus,

Take square roots, (note terms are non-negative),

This is,

if,

I did not yet complete the proof when,

I do not see how :(