hi to all can i please see the answer for this to check what i have been doing wrong thanks heaps. (a) Where is the function f(z) = z/(1+iz)^4 analytic? (b) Find f(-i).
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a) Plug f(z) in the Cauchy-Riemann equations and see where they are satisfied b) Replace z by -i
Originally Posted by sandy hi to all can i please see the answer for this to check what i have been doing wrong thanks heaps. (a) Where is the function f(z) = z/(1+iz)^4 analytic? (b) Find f(-i). Originally Posted by vincisonfire a) Plug f(z) in the Cauchy-Riemann equations and see where they are satisfied b) Replace z by -i What vincisonfire said is true, but surely you have proved that any rational function in is analytic everywhere it's denominator is non-zero, right?
Originally Posted by vincisonfire a) Plug f(z) in the Cauchy-Riemann equations and see where they are satisfied b) Replace z by -i can i please have a hint of how to break it up do i substitute z by x+iy but then its to big what do i do?
It is a bit messy. It may be simpler in this form :
Originally Posted by vincisonfire It is a bit messy. It may be simpler in this form : thanks so much for your help i done it and found that cauchy riemann equations are satisfied every where so do we say f(z) is analytic everywhere on C??
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