Question 11

Give the Taylor series, centered at the origin, for each of the following functions and for each determine, with proof, when the series converges:

• $f(z) = \ln(1 + iz)$
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• $g(z) = (1 - 2z)^{-2}$
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• $h(z) = e^z\cos(z)$.