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#1 2015-09-20 05:06:44

mrpace
Member
Registered: 2012-08-16
Posts: 88

Complex numbers algebra

Show that,

|1 − zw*|^2   −   |z − w|^2 = (1 − |z|^2)(1 − |w|^2)

where z and w are complex numbers and z* is the conjugate of z.

Not very fluent with algebraic properties of these things so please help!!
Thanks.

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#2 2015-09-20 05:40:49

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: Complex numbers algebra

Use the fact that
to get rid of the modulus signs on the LHS, then expand.

Last edited by zetafunc (2015-09-21 05:33:22)

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#3 2015-09-21 05:33:49

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Complex numbers algebra

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