Imaginary number is a number whose square is negative. The word imaginary number was founded by Descartes, a famous mathematician in the17th century, because the concept at that time thought it was a non-existent real number. Later, it was found that the imaginary number can correspond to the vertical axis on the plane, which is as real as the real number corresponding to the horizontal axis on the plane.

It is found that even if all rational numbers and irrational numbers are used, the problem of solving algebraic equations cannot be solved. Like x? The simplest quadratic equation+1=0 has no solution in the real number range. 12 century Indian mathematician Bashgaro thinks this equation has no solution. He thinks that the square of a positive number is a positive number and the square of a negative number is also a positive number. Therefore, the square root of a positive number is double; A positive number and a negative number, negative numbers have no square root, so negative numbers are not squares. This is tantamount to denying the existence of the negative square root of the equation.

/kloc-in the 6th century, Italian mathematician cardano recorded it as1545r15-15m in his book Great Skills, which is the earliest imaginative symbol. But he thinks this is just a formal expression. 1637, the French mathematician Descartes gave the name of "imaginary number" for the first time in Geometry, corresponding to "real number".

1545, cardano of Milan published the most important algebraic works in the Renaissance, and put forward the formula for solving the general cubic equation:

The cubic equation in the form of x3+ax+b=0 is solved as follows:

x = {(-b/2)+[(B2)/4+(a3)/27] 1/2 } 1/3+{(-b/2)-[(B2)/4+(a3)/27] 1/2 } 1/3

When Kadan tried to solve the equation x3- 15x-4=0 with this formula, his solution was: x = [2+(-121)] (1/3)+.

At that time, the negative number itself was questionable, and the square root of the negative number was even more absurd. So Cardin's formula gives x=(2+j)+(2-j)=4. It is easy to prove that x=4 is indeed the root of the original equation, but Kadan did not enthusiastically explain the appearance of (-12 1) 1/2. Think of it as "unpredictable and useless."

It was not until the beginning of19th century that Gauss systematically used the symbol I, and advocated using a number pair (a, b) to represent a+bi, which was called a complex number, and the imaginary number gradually got through.

Because imaginary number has entered the field of numbers, people know nothing about its practical use, and there seems to be no quantity expressed by complex numbers in real life, so people have all kinds of doubts and misunderstandings about it for a long time. Descartes called it "imaginary number" because it is false; Leibniz thinks: "imaginary number is a wonderful and strange hiding place for gods." It is almost an amphibian that exists and does not exist. " Although Euler used imaginary numbers in many places, he said, "All mathematical expressions in the form of √- 1 and √-2 are impossible, imaginary numbers, because they represent the square root of negative numbers. For such figures, we can only assert that they are neither nothing nor more than nothing, nor less than nothing. They are purely illusory. "

After Euler, the Norwegian surveyor Wiesel proposed that the complex number (a+bi) should be represented by points on the plane. Later, Gauss put forward the concept of complex plane, which finally made complex numbers have a foothold and opened the way for the application of complex numbers. At present, vector (vector) is generally represented by complex numbers, which are widely used in water conservancy, cartography, aviation and other fields, and imaginary numbers are increasingly showing their rich contents.