If Pdx+Qdy is locally exact in R`,prove that [tex]\int[/tex]Pdx+Qdy=0 for every cycle Y-0 in R`.
I'm a bit confused by this. You titled this "complex analysis". But refer to an integration in "R`" and appear to have a real integrand.
What, exactly, is your definition of "locally exact" and what do you mean by "R1"?
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