The points on the horizontal axis of the complex plane correspond to all real numbers, so it is called the real axis, and the points on the vertical axis (except the origin) correspond to all pure imaginary numbers, so it is called the imaginary axis. On the complex plane, the complex number also corresponds to the plane vector from the origin to the point z=x+iy, so the complex number z can also be represented by the vector z (as shown in the right picture). The length of the vector is called the modulus or absolute value of z, and it is denoted as | z | = r = √ (x 2+y 2). In addition to the works of Wiesel (1745- 18 17) and Argonne (1768- 1822), there are also Coates (1707-/kloc). Vandermonde (1735- 1796) also realized that points on the plane can correspond to complex numbers one by one, which was confirmed by the fact that they regarded the roots of binomial equations as vertices of regular polygons. However, Gauss's contribution is very important in this respect. His famous basic theorem of algebra is derived on the premise that points on the coordinate plane can correspond to complex numbers one by one. 183 1 year, Gauss explained in detail in Journal of Gottingen that the complex number a+bi is expressed as a point (A, B) on a plane, thus clarifying the concept of the complex plane, and he integrated the rectangular coordinates representing the plane points with the polar coordinates. Two representations of the same complex number-algebraic form and triangular form. Gauss also gave the name "complex number". Because of the outstanding contribution of Gauss, later generations often call the complex plane Gauss plane.