When solving equations, imaginary numbers are generated. When solving equations, it is often necessary to square the numbers. If the root number is not negative, the required root can be calculated; What if it is negative?

For example, if the equation x2+ 1=0, then x2=- 1 and x =+- 1. So-1 Does it make sense? A long time ago, most mathematicians thought that negative numbers had no square root. By the middle of16th century, Italian mathematician Caldan published his mathematical work Dafa, and introduced the formula for finding the roots of cubic equations. He discussed not only positive roots and negative roots, but also imaginary roots. If we solve the equation x3- 15x+4=0, according to his root formula, we will get:

X=-2+- 12 1 where-12 1 is the square root of a negative number. Caldan wrote the square root of a negative number, but he thought it was just a formal expression. It shows that he doesn't understand the nature of the square root of negative numbers. 1637, French mathematician Descartes began to use the terms "real number" and "imaginary number". 1777, the Swiss mathematician Euler began to use the symbol i=- 1 to express the unit of imaginary number. Then people combine real numbers and imaginary numbers to write a+bi (both a and b are real numbers), which is called complex number.

When imaginary numbers broke into the field of mathematics, people knew nothing about its practical use, and there seemed to be no quantity expressed by complex numbers in real life. Therefore, for a long time, people have all kinds of doubts and misunderstandings about imaginary numbers. Descartes said that "imaginary number" originally meant that it was false; Leibniz thought at the beginning of18th century: "Imaginary number is a wonderful and strange secret hiding place. It is almost an amphibian that exists and does not exist." Although Euler used imaginary numbers in many places, he also said that all mathematical formulas in the form of-1 and -2 are impossible and purely illusory.

After Euler, the Norwegian surveyor Wiezell proposed that the complex number a+bi be represented by points (a, b) 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, vectors are generally represented by complex numbers, which are widely used in hydraulics, cartography and aeronautics. Imaginary number shows its rich content more and more, which is really: imaginary number is not empty!