I recently came across this question:

Find the number of elements in the following cyclic group:

The cyclic sub-group of $C^{*}$ generated by 1+i

The solution says the answer is: O(Z), where Z is the set of all natural numbers. It further says this is so because $|1+i|=\sqrt{2} >1$.

I couldn't get it intuitively. Why does the order have to be O(Z)?

Can anyone please help?

Thanks in advance!


1 Answer 1


If $z=1+i$, then $|z|=\sqrt2>1$. Then $|z^2|>|z|$, $|z^3|>|z^2|$, and so on. So, $C^*$ is an infinite cyclic group, and therefore it is isomorphic to $(\Bbb Z,+)$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.