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anonymous

  • one year ago

|f| = e^(x^2 - y^2), find f?

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  1. anonymous
    • one year ago
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    @oldrin.bataku could you help me with this question please?

  2. anonymous
    • one year ago
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    so |f| = sqt of u^2 + v^2=e^(x^2 - y^2) how can i calculate u and v?

  3. Sachintha
    • one year ago
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    @ganeshie8

  4. Sachintha
    • one year ago
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    @Jhannybean

  5. Sachintha
    • one year ago
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    I think there are some data missing. o.O

  6. anonymous
    • one year ago
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    no the question is like this

  7. triciaal
    • one year ago
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    |dw:1443419852653:dw|

  8. anonymous
    • one year ago
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    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

  9. anonymous
    • one year ago
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    thanks a lot

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