Extension of number system and complex number It is known that the locus of the corresponding point of the complex Z satisfying the cubic power of | Z | - 2 | Z | - 3 = 0 is () A1 circle B segment C 2 points D 2 circles

Extension of number system and complex number It is known that the locus of the corresponding point of the complex Z satisfying the cubic power of | Z | - 2 | Z | - 3 = 0 is () A1 circle B segment C 2 points D 2 circles

From the answers you gave, it seems that the title should be | Z | & sup2; - 2 | Z | - 3 = 0
If so, the original formula is (| Z | + 1) (| Z | - 3) = 0
And | Z | ≥ 0, so | Z | = 3 represents a circle
If according to the original problem, Let f (x) = x & sup3; - 2x-3, X ≥ 0. It is easy to obtain that f (x) increases monotonically in the interval [0, √ 6 / 3], decreases monotonically in the interval [√ 6 / 3, + ∞). And f (0)

After the complex number, what number has the present number system expanded to? What is the significance of its expansion?

The range of complex numbers is closed to general operations. However, if the vector is also understood as a number, then the complex number still needs to be expanded, and there is a corresponding number system - quaternion

On the extension of number system and the concept of complex number
3I ^ 2 = - 3, is it a real number?
Why and how

The range of numbers we are learning now is the range of real numbers. A real number is a certain number (including rational numbers and irrational numbers). 3I ^ 2 = - 3 is a certain value. Even if you can't find it, but the number exists and the size will not change, then it is a real number. This is the same as the root power of a certain number, although it can't be calculated, But it can be approximated infinitely by dichotomy. It is also a definite real number