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anonymous
 one year ago
f = e^(x^2  y^2), find f?
anonymous
 one year ago
f = e^(x^2  y^2), find f?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@oldrin.bataku could you help me with this question please?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so f = sqt of u^2 + v^2=e^(x^2  y^2) how can i calculate u and v?

Sachintha
 one year ago
Best ResponseYou've already chosen the best response.0I think there are some data missing. o.O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no the question is like this

triciaal
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443419852653:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0consider $$f=u+iv\\f^2=(u+iv)(uiv)$$ so we have $$(u+iv)(uiv)=e^{2(x^2y^2)}$$now consider \(2(x^2y^2)=(x^2+2ixyy^2)+(x^22ixyy^2)=(x+iy)^2+(xiy)^2\) so we can factor our righthand side like so: $$e^{2(x^2y^2)}=e^{(x+iy)^2}e^{(xiy)^2}$$so we could have that \(f(z)=e^{z^2}\) and \(f^*(z)=\overline{(e^{z^2})}=e^{(\bar z)^2}\), which checks out
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