A Visual Intro to Complex Numbers

Complex numbers were developed to solve equations that have no solutions using only real numbers, such as those requiring the square root of negative values. Italian mathematician Gerolamo Cardano first encountered this problem in 1545 while solving cubic equations, discovering that some real solutions required intermediate steps involving square roots of negative numbers. This mathematical necessity eventually led to the creation of the complex number system, which extends real numbers to make these previously impossible calculations feasible.