I have this problem without a solution (yet)
Say I have a complex number and wish to calculate $\phi(a+bi)$ where $\phi(n)$ is Euler's totient function. How would it have to be calculated? I know that $\phi(n)$ calculates the amount of integers below n that are coprime to n. But since complex numbers form a field, what defines 'below' and what defines 'coprime'?
Thanks in advance :)
The complex numbers I am using are all Gaussian Integers