1. unitary automorphism: This is the simplest automorphism, which maps each complex number to itself. This automorphism keeps the addition and multiplication operations of complex numbers unchanged.

2. Translational automorphism: This automorphism translates the points on the complex plane according to a certain direction and distance. For example, the points on the complex plane are translated according to the vector (a, b) to obtain a new complex domain, in which each complex Z is mapped to z+a+bi. This automorphism keeps the addition and multiplication operations of complex numbers unchanged.

3. Rotational automorphism: This automorphism rotates a point on the complex plane by a certain angle. For example, a point on the complex plane is rotated counterclockwise by θ radians, and a new complex field is obtained, in which each complex Z is mapped to E (I θ) Z. This automorphism keeps the addition and multiplication operations of complex numbers unchanged.

4. Scaling automorphism: This automorphism scales the points on the complex plane according to a certain proportion. For example, if the points on the complex plane are scaled by the factor r, a new complex number field is obtained, in which each complex number z is mapped to r z. This automorphism keeps the addition and multiplication operations of complex numbers unchanged.

5. Reflective automorphism: This automorphism reflects the points on the complex plane about the real axis or imaginary axis. For example, by reflecting points on the complex plane about the real axis, a new complex number field is obtained, in which each complex number z is mapped to conj(z), where conj stands for * * * yoke. This automorphism keeps the addition and multiplication operations of complex numbers unchanged.

These are some common automorphisms of complex fields. It should be noted that these automorphisms keep the addition and multiplication operations of complex numbers unchanged, because in mathematics, we usually only care about those structural transformations that keep some operations unchanged.