How a 1545 Math Trick Turned the Impossible Square Root of -1 into a 2D Revolution
A Visual Intro to Complex Numbers
Starting with an unsolvable system of equations, this visual essay traces complex numbers from Gerolamo Cardano's 1545 dilemma—needing the square root of -15 to solve real problems—through René Descartes' dismissive 'imaginary' label, Leonhard Euler's notation i, and the Argand–Wessel plane that maps complex numbers as points. It shows how multiplying by i is a 90-degree rotation, making the imaginary dimension a natural extension of the real number line.
He viewed the whole maneuver as a mere “convenient artifice”— a mathematical magic trick with no actual substance or practical meaning behind it.