Calculate the root of a negative number. It is meaningful in mathematics, but it is meaningless in nature. To trace the trajectory, it is necessary to contact the appearance process of its relative real number. We know that real number corresponds to imaginary number, which includes rational number and irrational number, that is, it is real number. Rational numbers appeared very early, accompanied by people's production practice. The discovery of irrational numbers should be attributed to the Pythagorean school in ancient Greece. The appearance of irrational numbers contradicts democritus's "atomism". According to this theory, the ratio of any two line segments is the number of atoms they contain. However, Pythagorean theorem shows that there are incommensurable line segments. The existence of incommensurable line segments made the mathematicians in ancient Greece feel in a dilemma, because their theory only had the concepts of integer and fraction, and could not fully express the ratio of diagonal to side length of a square, that is to say, in their place, the ratio of diagonal to company commander of a square could not be expressed by any "number". They have discovered the problem of irrational numbers, but let it slip away from them. Even for Diophantine, the greatest algebraic scientist in Greece, the irrational solution of the equation is still called "impossible". The determination of irrational numbers is closely related to the root operation. For those incomplete square numbers, it is found that their square roots are infinite acyclic decimals with any number of digits. (For example, π = 3. 14 1592625 …, E=2. 7 1828 182, etc. ), called irrational number. But when the position of irrational numbers is determined, it is found that even if all rational numbers are used and nothing is used, the problem of solving algebraic equations cannot be solved in length. The simplest quadratic equation, such as x 2+ 1=0, has no solution in the range of Lu. 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 negative roots of the equation. /kloc-in the 6th century, cardano boldly used the concept of negative square root for the first time in Da Yan Shu. If you don't use the square root of a negative number, you can solve the quartic equation. Although he wrote the square root of negative discharge, he hesitated. He had to declare that this expression was fictitious and imaginary, and he never called it "imaginary" once. But mathematicians are still very cautious when using it. Even the famous mathematician Euler had to add a note to his paper when using imaginary numbers. The mathematical formulas in the form of √- 1 and √-2 are impossible numbers and 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 linear and illusory. Although this passage of the master is a bit awkward to read, it can be seen that he is not so confident about imaginary numbers. However, the emergence of imaginary numbers has greatly helped irrational numbers. Compared with rational numbers, irrational numbers are somewhat weak, but in the face of imaginary numbers, they are all real numbers like rational numbers, so mathematicians call them real numbers together with rational numbers to distinguish them from imaginary numbers. Interestingly, imaginary numbers are also tenacious. Just like the reflection of real numbers in the mirror, it is not only inseparable from real numbers, but also often combined with real numbers to form complex numbers. Imaginary number, people began to call it "the ghost of real number", Descartes called it "imaginary number" in 1637, so all imaginary numbers have BI, while complex numbers have a=bi, where A and B are real numbers. Imaginary numbers are also often called pure imaginary numbers. Since cardano's Da Yan Shu, imaginary numbers have been shrouded in mystery for 200 years. By 1797, wessel gave the image representation of the dotted line, and the reasonable position of the imaginary number was established. Together with Algan, he gave the geometric explanation of complex numbers with the help of the plane coordinate system established by Descartes, a French mathematician in the17th century, which is recognized by the mathematical community. Later, Gauss established a one-to-one correspondence between points and complex numbers on the rectangular coordinate plane, and imaginary numbers were widely known.