2. Within the range of complex numbers, even roots can be negative and odd roots can be negative. Because the complex number has already defined I? =- 1, so -2 can open the root sign, and √ (-2) = √ 2i.
I is an imaginary unit. At this time -√2 is a real number, and √-2 is an imaginary number, which has completely different meanings.
3. Extended information:
The root sign is a mathematical symbol. The root sign is a symbol used to represent the root operation of a number or an algebra. If a? =b, then A is the n-th root of B or A is the 1/n power of B. The n-th handwritten and printed characters are represented by, and the number of roots or algebraic expressions are written in the area surrounded by the left side of the symbol and the right side of the horizontal part above the symbol, which cannot be out of bounds.
In the range of real numbers,
(1) Even root number cannot be negative, and its operation result is not negative.
(2) It can be negative under odd root sign.
Not limited to real numbers, that is, when considering imaginary numbers, even roots can be negative numbers, and i=√- 1 can be used.
In a complex field, the square root of a negative number-1 is expressed as I (i.e. I? =- 1), called imaginary number or imaginary unit. A real number multiplied by I is called pure imaginary number. For example, 5i is a pure imaginary number.
Establish a rectangular coordinate system to represent complex numbers. The plane is called the complex plane, the X axis is called the real axis, and the Y axis is called the imaginary axis. In this way, all points on the real axis represent real numbers, and all points on the imaginary axis represent pure imaginary numbers except the origin.
A number in the form of a+bi(a, b∈R) is called a complex number, where A is the real part of the complex number and B is the imaginary part of the complex number. The set composed of all complex numbers is called a complex number set, which is represented by the letter C.
Complex number a+bi(a, b∈R) is a real number when b=0; When b≠0, it is called imaginary number; When a=0 and b≠0, it is called pure imaginary number.
Representing a complex number as a+bi(a, b∈R) is called the algebraic form of a complex number.
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