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

1. anonymous

@oldrin.bataku could you help me with this question please?

2. anonymous

so |f| = sqt of u^2 + v^2=e^(x^2 - y^2) how can i calculate u and v?

3. Sachintha

@ganeshie8

4. Sachintha

@Jhannybean

5. Sachintha

I think there are some data missing. o.O

6. anonymous

no the question is like this

7. triciaal

|dw:1443419852653:dw|

8. 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

9. anonymous

thanks a lot