In mathematics, imaginary numbers are numbers in the form of a+b*i, where a and b are real numbers, b≠0, i? = - 1
When the unary quadratic equation is in the calculation formula "b? -4ac & lt； 0, the equation represents no solution in the real number range, but in the complex number range, the imaginary number in the complex number can be used to represent the solution of the equation.
As far as the theme is concerned, the third grade does not involve complex numbers, and the normal solution of the equation is no solution.
If you have to write an answer, then the answer is in the plural range:
X 1=- 1/4+√23/4i
X2=- 1/4-√23/4i
The complex number X is defined as a binary ordered real number pair (a, b), denoted as z=a+bi, where a and b are real numbers and I is an imaginary unit.
In the complex number a+bi, a=Re(z) is called the real part, and b=Im(z) is called the imaginary part.
When the imaginary part is equal to zero, this complex number can be regarded as a real number; When the imaginary part of z is not equal to zero and the real part is equal to zero, z is often called pure imaginary number. Complex number field is an algebraic closure of real number field, that is, any polynomial with complex coefficients always has roots in complex number field.
Complex number was first put forward by Cardan, a scholar in Milan, Italy, in the16th century. Through the work of D'Alembert, De Moivre, Euler and Gauss, this concept was gradually accepted by mathematicians.
The four operations of complex numbers are as follows: addition rule: (a+bi)+(c+di) = (a+c)+(b+d) i.
Subtraction rule: (a+bi)-(c+di) = (a-c)+(b-d) i.
Multiplication rule: (a+bi) (c+di) = (ac-bd)+(bc+ad) i.
Division rule: (a+bi)÷(c+di)=[(ac+bd)/(c? +d？ )]+[(bc-ad)/(c？ +d？ )] me