Question

Let H={a+bi a,b is a element R, a^2+b^2=1} be a subset of the non zero complex numbers C*. Prove that H<C* under complex multiplication using the one-step subgroup test. Also describe the elements of H geometrically.

Answer 1

The elements of H are the complex numbers on the unit circle and if you multiply two of those you get another complex number on the unit circle, so the product of two elements of H is another element of H.