Complex Analysis     MATH 305

Homework Assignment #1

Due Thursday, Jan. 28, START of Class

Watch the YouTube video e to the pi i for dummies, posted by the Mathologer, which gives a derivation that "even Homer could understand" for the famous formula eπ i + 1 = 0. Then answer the following questions (write legibly or type your answers up).

  1. What do you like about the video? What are some of the strengths of the presentation?
  2. State something new and/or interesting you learned from the video.
  3. One of the key arguments in the explanation of the formula is visualizing complex multiplication via geometric manipulation of triangles. Later we will explain why this technique works. Carefully watch how 1 + 2i is multiplied by 1 + 1.5i using triangles. Draw a few diagrams (use color!) to illustrate the calculation of (1 + i)2 using triangles.