What does Arg mean in mathematics? mathematics

What does Arg mean in mathematics? mathematics

arg:argument of The argument of a complex number
For example:
z = r*(cosθ + i sinθ)
R is the module of Z, that is: r = | Z |;
θ is the radiation angle of Z, denoted as: θ = Arg (z)
See?

The negative value problem of COS function of Arg (- 1 + 2I)
Why does this cos function have a negative sign? Please let me know in detail
a=arg（2+i）b=arg(-1+2i)
Why does this cos function have a negative sign?

Let's take - 1 + 2I as a point on the complex plane, which is (- 1,2). Let's record it as point P, connect OP, and what we want is the cosine of the angle XOP, which is an angle of the second quadrant, so it is negative

Given | Z | = √ 2, the maximum value of Arg (z-2i) is
A7π/4,B5π/4,C3π/4Dπ/4

|Z | = √ 2, which means that the point P corresponding to complex Z moves on the circle (with origin o as the center and √ 2 as the radius), while z-2i can be expressed as the vector AP whose fixed point a (0,2) corresponding to 2I points to P. when the main value of the argument of vector AP corresponding to all complex z-2i is the largest, the tangent of AP and circle O (the tangent point is on the right side of Y axis) is related by the corner in the right angle △ apo