Let a = {Z | Z-2 + I | be less than or equal to 2, Z belong to C}, B = {Z | z-2-i | = | Z-4 + I |, Z belong to C}, let m = ab (1) Determine the locus of the point corresponding to the complex number in the complex plane (2) Find the value range of modulus of complex Z in set M PS：

Let a = {Z | Z-2 + I | be less than or equal to 2, Z belong to C}, B = {Z | z-2-i | = | Z-4 + I |, Z belong to C}, let m = ab (1) Determine the locus of the point corresponding to the complex number in the complex plane (2) Find the value range of modulus of complex Z in set M PS：

(1) The trajectory of a is a circle and its interior with (2, - 1) as the center and 2 as the radius, and the trajectory of B is the vertical bisector of C (2,1) and D (4, - 1), so the trajectory of M is a line segment. The product of the slope K of this line segment and the slope of CD is - 1, and K = 1 can be calculated. Moreover, if it passes through the midpoint (3,0) of CD, the equation of the line segment is x-y-3 = 0. If this equation and the equation of circle (X-2) ^ 2 + (y + 1) ^ 2 = 2, x = 1 or 3 can be obtained, So the final trajectory is x-y-3 = 0 (x is greater than or equal to 1, less than or equal to 3)
(2) It can be found that the minimum is the distance from the origin to the straight line x-y-3 = 0, and the calculated distance d = 1.5 times of the heel 2. The maximum should be the distance from the origin to (3,0) 3, that is, the value range of the modulus is the closed interval [1.5 times of the heel 2,3]

We all know that the square of I is equal to - 1. If so, why is it still a pure imaginary number

The symbol I [where I = √ (- 1)] represents the unit of an imaginary number. Later, people organically combined the imaginary number with the real number and wrote it in the form of a + bi, where a is called the real part of the imaginary number, B is called the imaginary part of the imaginary number, and a and B are both real numbers. When the real part of the imaginary number is 0 and the imaginary part is not 0, the number whose square is negative is defined as a pure imaginary number

How to express complex number in MATLAB
s=i;
>> real(s)
ans =
one
how to deal with it

Did you define I as a variable before
Using s = 1I