The Beautiful Geometry of Complex Numbers and Quadrilaterals (3 Blue1 Brown So ME1)

Use the algebra and geometry of complex number addition, subtraction, and multiplication to prove a surprising relationship between squares on the sides of any quadrilateral. Visual Complex Analysis, by Tristan Needham: My math blog: This is my submission for 3Blue1Brown s SoME1: Original Title: The Beauty is in the Proof Complex Numbers and Quadrilaterals (3Blue1Brown SoME1). Changed the name in the morning on Sunday, November 21, 2021. , 3Blue1Brown, SoME1, SummerOfMathExposition Visual Complex Analysis, by Tristan Needham: Complex Numbers are Real at Infinity is Really Big: The line segments between midpoints of squares on the opposite sides of a quadrilateral are perpendicular to each other and have the same length. The geometry of complex number of arithmetic can be used to prove this. If we represent c