Infinite Limit Complex Function

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Homework Help Overview

The discussion revolves around finding the limit of a complex function as the variable approaches infinity, specifically examining the expression (8z^3 + 5z + 2) as z approaches infinity.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss splitting the complex function into real and imaginary parts and question how to handle the limit as z approaches infinity. There is also a consideration of the implications of |z| approaching infinity and its effect on the limit of the function.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the limit and clarifying the meaning of "z approaches infinity" in the context of complex numbers. Some guidance has been offered regarding the behavior of the function's components as they approach infinity.

Contextual Notes

There is a recognition that in the complex plane, the concept of infinity may have multiple interpretations, which adds complexity to the problem at hand.

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Homework Statement


Find the limit of a complex number involving infinity.


Homework Equations


Lim z->infiity of (8z^3+5z+2)


The Attempt at a Solution


I tried to split the problem into real and imaginary parts using z = x+iy, but I don't know how to deal with the z->infinity.

Thanks!
 
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I could be misreading the problem, but the real part and imaginary part of that equation will go to infinity as well no matter which you take.
 
z->infinity means |z|->infinity. What can you say about lim |8z^3+5z+2|?
 
Thanks, Dick. I was about to ask exactly what "z-> infinity" meant! In the complex plane there can be an infinite number of "infinities"!
 

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