Daily Assignment for Friday, February 28

Due Monday, March 3 on Canvas.

• Here are the two Desmos visualizations from Friday's class.
• At the end of class, we considered a function \( f_c(z) = z^2 + c \) and asked when \( f_c \) has an attracting fixed point. This means a point \( z_0 \) such that \( f_c(z_0) = z_0 \) and \( |f'(z_0)| \le 1 \). To answer this question, first find the fixed points of \( f_c \) in terms of \( c \). Then compute \( f'(z_0) \) for each of these fixed points. Finally, plot on the complex plane the values of \( c \) for which \( f_c \) has an attracting fixed point.
• Read §§7.1 and 7.2 of Needham.
• 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.