Determine a so that the function is harmonic and find a harmonic conjugate.

  • Determine a so that the function is harmonic and find a harmonic conjugate.

 

  • Find the Taylor series of with center .

 

 

  • Find all Taylor and Laurent series of Determine the precise region of convergence. Show details.

 

  • Determine the locations of singularities, including those at infinity, also state the order of poles for .

 

 

  • Evaluate Integrate C the unit circle.

 

  • Evaluate .