the.com/complex plane

means A two-dimensional coordinate plane for graphing complex numbers, where the horizontal axis holds the real part and the vertical axis holds the imaginary part.

from The idea took shape around the turn of the 19th century, credited mainly to Caspar Wessel, Jean-Robert Argand, and later Carl Friedrich Gauss (whose name sticks to the 'Gauss plane' in some languages). Before this, 'imaginary' numbers like the square root of -1 had no home — they worked in equations but couldn't be pointed to. Argand and the others realized that treating the imaginary unit as a perpendicular axis, rather than a point on the ordinary number line, let every complex number a + bi correspond to a literal point (a, b). 'Complex' here comes from the Latin complexus, 'woven together' — fitting, since these numbers braid a real and imaginary part into one object. The plane didn't change the math; it just gave the math a map.