Daily Assignment for Wednesday, January 15

Due Friday, January 17 on Canvas.

• Take another look at the practice problems in §1.1.4. Can you find geometric and algebraic explanations for all of them ? The Desmos project from class may be helpful :
• Read §§1.2 and 1.3.2 of Needham's book.
• In §1.1.1, Needham says that Euler mistakenly asserted that \( \sqrt{-2} \sqrt{-3} = \sqrt{6} \). What was Euler's mistake ?
• Do exercises 6, 7, and 10 from p. 52 of Needham's book. Hint for #10 : \( (z + 1) = z(1 + z^{-1}) \).
• Find all complex numbers \( z \) that satisfy the equation \( z^{12} = 1 \).
• 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.