Daily Assignment for Monday, January 13

Due Wednesday, January 15 on Canvas.

• Make sure you can access the course webpage, Canvas, the textbook, the other textbook, and Discord (see Canvas for the invitation).
• Read §§1.1.3-1.1.5 of Needham.
• Do the practice in §1.1.4. Take your time and try to appreciate the meaning of each statement both geometrically and algebraically.
• Do exercise 5 in §1.5 on p. 52.
• Check the formula \( ( r \angle \theta)(s \angle \phi) = (rs) \angle (\theta + \phi) \) algebraically by multiplying out \( (r \cos(\theta) + i r \sin(\theta))(s \cos(\phi) + i s \sin(\phi) ) \). Look up the angle sum identities if you need to.
• Find a real 2×2 matrix \( A(r, \theta) \) that rotates counterclockwise by the angle \( \theta \) and scales by the real number \( r \). In other words, if \( v \) is any vector in \( \mathbb R^2 \) then \( A(r,\theta) v \) should be the vector obtained from \( v \) by rotating through the angle \( \theta \) and scaling by \( r \). Compare \( A(r,\theta) A(r',\theta') \) to \( (r \angle \theta )(r' \angle \theta') \) and compare \( A(r,\theta) + A(r',\theta') \) to \( (r \angle \theta) + (r' \angle \theta') \).
• 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.