Question

show that the set H= a +ib belongs to (C *| a2 +b2 = 1) is a subgroup of (c*,.) where . is usual multiplication of complex numbers.

Answer 1

Answer:

Consider

Clearly, 1+ 0i is a member of H and so, H is a non empty subset of the multiplicative group of non zero complex numbers

Suppose are any members of H

Then by definition, are real numbers such that