In the complex field, the imaginary part of the constant c is zero, which can be regarded as a real number; But the real part of ic is zero, which is pure imaginary number.

Complex number (conceptual extension of number)

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 stipulated 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.

For example: [(a+bi)+(c+di)]-[(a+c)+(b+d) i] = 0, and the final result is still 0, so there is no complex number in the number.

[(a+bi)+(c+di)]-[(a+c)+(b+d) i] = z is a function.