C* is the group of all non-zero complex numbers under multiplication

H: C*---->C*

z----->zz (second z is complex conjugate of complex number z)

This is a homomorphism.

The identity element in (C*,x) is 1, so

Ker H = {z E C* : H (z) = 1}

= {z E C* : zz = 1}

= { z E C* : z = z}

= R+

Because z = z (complex conjugate) for each z E C*, the function H is onto and

Im(H) = C*.

Is this correct?

Also I need to find a group with is isomorphic to Ker (H).