Daily Assignment for Wednesday, March 5

Due Friday, March 7 on Canvas.

• Read §7.5.1.
• The fundamental theorem of algebra says that if \( f \) is a nonconstant polynomial with complex coefficients then there is some \( z \in \mathbb C \) such that \( f(z) = 0 \). Use the argument principle and the fact \( \nu(f \circ \gamma, 0) = \deg(f) \) when \( \gamma \) is a large loop around \( 0 \) to prove the fundamental theorem of algebra. See §7.5.2 for the answer.
• Do exercise 22 on pp. 426–427. This reviews the proof of the argument principle from class.
• Do exercise 3 on p. 421.
• You may want to reread §7.4.4. We will discuss this proof in class on Friday.
• 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.