I sometimes find my attention hijacked by video game sales. If I find a huge number of games on sale, I sometimes lose my mind for the next eight to ten hours. I must amass a list and narrow it down. This process goes downhill quickly. First I pick up
(Or: Why not lurk?) (See also: Zvi Mowshowitz on You're Good Enough You're Smart Enough and People Would Like You, D. R. MacIver on You should write more and again, plus that guide to writing every day.) I often find myself lurking, in the sense of
Last time we made a geometric argument that given four complex numbers \(A, B, C, D\) lying on the unit circle, if they satisfy \(A + B + C + D = 0\), then they form a rectangle. Okay, technically, I didn't show the rectangle part. I did show the segments are
I want to return to yesterday's problem from Visual Complex Analysis. Suppose we have four complex numbers \(A, B, C, D\) on the unit circle such that \(A + B + C + D = 0\). We want to show that these points must form a rectangle. How can we do this?
There's an exercise that's bugged me for a while from Tristan Needham's Visual Complex Analysis. It's a proof exercise: Prove that for complex numbers \(A, B, C, D\) lying on the unit circle (so magnitude 1), if \(A + B + C + D = 0\