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Dividing by Zero=undefined or complex infinite? 
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#1
Mar812, 11:24 PM

P: 57

A few days ago, I had a problem that looked like this:
evaluate cot(pi) I know that on the unit circle, cot(pi) ends up as 1/0. In my precalc class, we say that this is undefined because you can't divide by zero. I decided to plug the problem into wolfram and it tells me that there is in fact an answer, that being complex infinity. I'm not sure what to make of this as I've never heard of complex infinity. Am I wrong to say that cot(pi), or any other number divided by zero is undefined, or is the correct answer complex infinite? Thanks! 


#2
Mar812, 11:44 PM

P: 800

Here's a page that reveals all. http://en.wikipedia.org/wiki/Riemann_sphere 


#3
Mar812, 11:59 PM

P: 57

Thank you 


#4
Mar912, 12:18 AM

P: 4,579

Dividing by Zero=undefined or complex infinite?
Hey physicsdreams. A complex number is written in the form of z = a + bi where a and b are just real numbers. The infinitecomplex number is just a number that has an infinite 'length'. We define the 'length' of a complex number to be SQRT(a^2 + b^2). Basically if you look at the RiemannSphere wiki that was posted above, this 'infinite' complex number is at the point where the 'north pole' is, and the complex number that is 'zero' (i.e. z = 0 + 0i = 0) is at the south pole. 


#5
Mar912, 12:21 AM

P: 800

This is somewhat advanced math, typically taken by undergrad math majors after a couple of years of calculus and a class in real analysis. It would never be accurate to say you can divide by zero. Perhaps Wolfram should do a better job of explaining what they're doing so as not to confuse people who haven't taken a course in complex variables. 


#6
Mar912, 12:37 AM

P: 57

Thank you all for your explanations.
Hopefully I'll gain a better understanding of this advance concept in the future. 


#7
Mar912, 12:56 AM

P: 772

It's undefined when working with the reals. I don't think there's any reason to get into anything more complex at this point (certainly not complex analysis).



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