Multiplication Through Imaginary Numbers

This painting by Crockett Johnson in 1967 is from the National Museum of American History. It was inspired by ideas of Carl Friedrich Gauss on the Fundamental Theorm of Algebra and his work on imaginary numbers. Gauss showed that just as real numbers can be represented on a number line, complex numbers can also be represented on a coordinate plane. Eric Temple Bell in J. R. Newman's The World of Mathematics  expands on this idea and this painting is strongly inspired by a figure in his article. 

This is the figure that inspired this painting.