Daily Assignment for Friday, January 31

Due Monday, February 3 on Canvas.

• Explain in your own words why \( \sqrt{z} \) cannot be defined continuously on any region in \( \mathbb C \) that includes a loop around the origin.
• Find the power series of \( (z + a )^{1/2} \). What is its radius of convergence?
• The function \( f(z) = z^{1/3} \) is continuous for all real values of \( z \). Can it be defined continuously for complex values of \( z \)?
• Find the power series of \( (z+a)^{1/3} \) and determine its radius of convergence. What seems to be obstructing the convergence?
• Finish reading §2.6 if you haven't already and start §2.7.
• Assign yourself a grade for this assignment :
  1. At least 60 minutes.
  2. About 45 minutes.
  3. About 30 minutes.
  4. About 15 minutes.
  Submit your grade as a submission comment with your assignment. This comment must be the first comment and it must be exactly 1 character long or the grade won't be registered.