Finding the Antiderivative of a complex functionI need to find the antiderivative of f ( z ) = z log ⁡ ( z ), but I am confused on how exactly to do that.So we need to find ∫ z log ⁡ ( z ) d z right? Since z = x + i y, then ∫ ( x + i y ) log ⁡ ( x + i y ) ( d x + i d y ), but then how do we split log ⁡ ( x + i y )?Can we just integrate normally with respect to z THEN substitute with z = x + i y? We can use integration by parts as usual if so.

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Finding the Antiderivative of a complex functionI need to find the antiderivative of   f  (  z  )  =  z  log  ⁡  (  z  ), but I am confused on how exactly to do that.So we need to find   ∫  z  log  ⁡  (  z  )  d  z right? Since   z  =  x  +  i  y, then   ∫  (  x  +  i  y  )  log  ⁡  (  x  +  i  y  )  (  d  x  +  i  d  y  ), but then how do we split   log  ⁡  (  x  +  i  y  )?Can we just integrate normally with respect to z THEN substitute with   z  =  x  +  i  y? We can use integration by parts as usual if so.

bgu999dq · Accepted Answer

Explanation:What about   F  (  z  )  =                    z        2            log      ⁡              z              2    −            z      2        4   one can easily check that by deriving F, one gets:      F    ′    (  z  )  =  f  (  z  )and how to get F ? the same as for real functions integrating by parts for example.

Finding the Antiderivative of a complex function I need to find the antiderivative of f (

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