Tan(pi/2)=complex infinity why?

[GreenPrint]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[gb7nash]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

It depends what number system you're working in.

Real numbers: undefined

Extended real numbers: infinity

Riemann sphere: infinity

 

[GreenPrint]

Interesting, thanks!