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Wednesday, November 06, 2013

 

|z|2=z¯z

It's rather easy to show that:
  |z|2=z¯z where z=x+iy
How about:
  |z+1|2=(z+1)(¯z+1)
?

As a challenge, consider:
  Re(ezz+1)=(e|z|2+x|z+1|2)cos(y|z+1|2)
where the left hand side refers to the real part of ezz+1. Does the equation hold ? Note in particular the right hand side is a real number, but in terms of numbers in the complex plane !

More at Analysis of a Complex Kind.


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