Why do we set z = cos α + sin β I in some high school plural questions, and if | Z-2 | = 2, why set 2 + cos α + sin α I QAQ, the concept is a little vague,

Why do we set z = cos α + sin β I in some high school plural questions, and if | Z-2 | = 2, why set 2 + cos α + sin α I QAQ, the concept is a little vague,

This is to calculate the complex number Z = cos α + sin β I. The formula is very strange, so I will just take Z as a vector, multiply cos α as a projection on the real axis, multiply sin α as a projection on the imaginary axis, multiply 1 on the real axis, multiply I on the imaginary axis, and add up to the vector Z
If | y | = 2, it is easy to understand that y means the circle with the origin as the circle point and the radius of 2 can be expressed as y = 2cos α + i2sin α, so that y = Z-2, that is, z = 2 + 2cos α + i2sin α, and then it is easy to calculate and understand