1797, Norwegian surveyor Wiezell submitted a paper "Analytical Representation of Direction, Especially Suitable for Determining Polygons on Plane and Sphere" to Danish Academy of Sciences. First of all, he proposed that complex numbers should be represented by points on the coordinate plane, established a one-to-one relationship between all complex numbers and points on the plane, and formed the concept of complex plane. But it did not attract attention at that time.
1806, a grandfather from Geneva published his paper "Imaginary Number, Its Geometric Interpretation" in Paris, and also talked about the geometric representation of complex numbers. He used the term "modulus" to represent the length of a vector, from which the term "modulus" came.
Gauss, a great German mathematician, is one of the founders of modern mathematics, and has a great influence in history, which can be juxtaposed with Archimedes, Newton and Euler. He already knows the geometric representation of complex numbers in 1799. In his three proofs of the basic algebra theorem of 1799, 18 15, 18 16, it is assumed that the complex number corresponds to the points on the rectangular coordinate plane one by one, but until 65438+. He said: "Today, people's consideration of imaginary numbers still boils down to a flawed concept, which casts a hazy and magical color on imaginary numbers. I think as long as+1,-1 and I are not called positive one, negative one or imaginary one, but positive one, negative one and horizontal one, then this hazy and magical color can disappear. " Later, people accepted the idea of complex plane, which some people called Gaussian plane. Using the geometric representation of complex numbers, complex numbers can be represented by vectors on the coordinate plane, and the addition of two complex numbers can be carried out according to the parallelogram rule of vector addition. A complex number multiplied by I (or -i) is equivalent to a vector representing the complex number rotating 90 counterclockwise (or clockwise). This makes many vectors in physics: force, velocity, acceleration, etc. Complex numbers can be used for calculation, making them an important tool in physics and other natural sciences.