Kevin Yang

💈 Polar & Complex Numbers

Third PSET of the year!

In the beginning of the unit, I was a bit confused why we were going to learn polar coordinates and review complex numbers at the same time, but after doing the PSET and witnessing the relationship between polar and complex, I am a strong proponent for complex numbers always being taught in conjugation with polar.

The relationship can best be seen through Euler's formula, which elegantly relates complex numbers with polar coordinates. What Euler did is remarkable and I spent a week trying to prove it by mapping a complex point to its corresponding point on a spiral (i.e e^(a+bi)). What I found was that the real portion of the complex becomes a scaler, while the imaginary portion of the complex becomes a vector. Thus in polar terms, scaler is the radius of the point and the vector is the angle. However, I seem to be missing some key insight that brings it all together. Anyways, this doesn't really relate to the PSET, but I thought it was worth mentioning 😀.

Note: The blank spots are where my graphs would go. As always, graphing in LaTex is not fun in the slightest, so I printed out the PSET and then graphed them in the blanks.

My Responses:🔗

Original PSET:🔗

Note: The problems of this PSET are not mine, they are my math teacher, Ryan Normandin's. All rights are reserved to him, reproductions of this PSET are forbidden.