tan(pi/2)=complex infinity... why?

GreenPrint

1. The problem statement, all variables and given/known data
Hi,

I have just now come to the realization that tan(pi/2) is not infinity but complex infinity. I was wondering why and can't seem to find the answer. I was told all through high school that tan(pi/2)=infinity or undefined but not complex infinity.

2. Relevant equations



3. The attempt at a solution

gb7nash

It depends what number system you're working in.

Real numbers: undefined

Extended real numbers: infinity

Riemann sphere: infinity

GreenPrint

Interesting, thanks!