anonymous
  • anonymous
|f| = e^(x^2 - y^2), find f?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
@oldrin.bataku could you help me with this question please?
anonymous
  • anonymous
so |f| = sqt of u^2 + v^2=e^(x^2 - y^2) how can i calculate u and v?
Sachintha
  • Sachintha

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Sachintha
  • Sachintha
Sachintha
  • Sachintha
I think there are some data missing. o.O
anonymous
  • anonymous
no the question is like this
triciaal
  • triciaal
|dw:1443419852653:dw|
anonymous
  • anonymous
consider $$f=u+iv\\|f|^2=(u+iv)(u-iv)$$ so we have $$(u+iv)(u-iv)=e^{2(x^2-y^2)}$$now consider \(2(x^2-y^2)=(x^2+2ixy-y^2)+(x^2-2ixy-y^2)=(x+iy)^2+(x-iy)^2\) so we can factor our right-hand side like so: $$e^{2(x^2-y^2)}=e^{(x+iy)^2}e^{(x-iy)^2}$$so we could have that \(f(z)=e^{z^2}\) and \(f^*(z)=\overline{(e^{z^2})}=e^{(\bar z)^2}\), which checks out
anonymous
  • anonymous
thanks a lot

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