Complex analysis (identity proof)












1












$begingroup$


I want to prove $|1-bar zw|=|1-zbar w|$.



The crux being $forall z,win mathbb C: bar zw=zbar w$



Work done so far: I tried breaking down $z$ and $w$ into its components and brute-force my way to validate the equality, but I was not able to prove it.



Any help will be greatly appreciated.






complex-numbers proof-writing







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$endgroup$

















    1












    $begingroup$


    I want to prove $|1-bar zw|=|1-zbar w|$.



    The crux being $forall z,win mathbb C: bar zw=zbar w$



    Work done so far: I tried breaking down $z$ and $w$ into its components and brute-force my way to validate the equality, but I was not able to prove it.



    Any help will be greatly appreciated.






    complex-numbers proof-writing







    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      I want to prove $|1-bar zw|=|1-zbar w|$.



      The crux being $forall z,win mathbb C: bar zw=zbar w$



      Work done so far: I tried breaking down $z$ and $w$ into its components and brute-force my way to validate the equality, but I was not able to prove it.



      Any help will be greatly appreciated.






      complex-numbers proof-writing







      share|cite|improve this question











      $endgroup$




      I want to prove $|1-bar zw|=|1-zbar w|$.



      The crux being $forall z,win mathbb C: bar zw=zbar w$



      Work done so far: I tried breaking down $z$ and $w$ into its components and brute-force my way to validate the equality, but I was not able to prove it.



      Any help will be greatly appreciated.






      complex-numbers proof-writing




      complex-numbers proof-writing






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      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 1 hour ago









      J. W. Tanner

      713111




      713111










      asked 2 hours ago









      Bertrand Wittgenstein's GhostBertrand Wittgenstein's Ghost

      440115




      440115






















          1 Answer
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          $begingroup$

          Hint:



          We have $|bar{x}|=|x|$. You just have to identify what should be the $x$ in your question.



          Also, in general, $bar{z}w ne zbar{w}$.






          share|cite|improve this answer









          $endgroup$













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            1 Answer
            1






            active

            oldest

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            active

            oldest

            votes






            active

            oldest

            votes









            5












            $begingroup$

            Hint:



            We have $|bar{x}|=|x|$. You just have to identify what should be the $x$ in your question.



            Also, in general, $bar{z}w ne zbar{w}$.






            share|cite|improve this answer









            $endgroup$


















              5












              $begingroup$

              Hint:



              We have $|bar{x}|=|x|$. You just have to identify what should be the $x$ in your question.



              Also, in general, $bar{z}w ne zbar{w}$.






              share|cite|improve this answer









              $endgroup$
















                5












                5








                5





                $begingroup$

                Hint:



                We have $|bar{x}|=|x|$. You just have to identify what should be the $x$ in your question.



                Also, in general, $bar{z}w ne zbar{w}$.






                share|cite|improve this answer









                $endgroup$



                Hint:



                We have $|bar{x}|=|x|$. You just have to identify what should be the $x$ in your question.



                Also, in general, $bar{z}w ne zbar{w}$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 2 hours ago









                Siong Thye GohSiong Thye Goh

                101k1466117




                101k1466117






























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