Daily Assignment for Monday, February 10

Due Wednesday, February 12 on Canvas.

• Suppose that \(a\), \(b\), and \(c\) are 3 distinct complex numbers. Show that the points \(z \in \mathbb C\) satisfying \( \mathrm{Im} \Bigl( \bigl( \frac{z-a}{z-b} \bigr) \bigl( \frac{c-a}{c-b} \bigr)^{-1} = 0 \) form either a circle or a line and that this circle or line contains \(a\), \(b \), and \(c \). Hint : interpret the equation as saying two angles are equal; why is this the equation of a circle ? This is discussed in §3.5.6, but you do not need to read the section to do the exercise. We will do this in class on Wednesday.
• Reading : we are still covering §§3.2 and 3.4.
• Do exercises 1 and 2 on p. 205.
• 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.