Limit of exp(z) (complex number)

In summary, the conversation discusses finding the limit as z approaches infinity for the function exp(z), where z is a complex number. The solution is that the limit does not exist, as e^iy oscillates and does not approach infinity for large y values. The conversation also mentions considering specific cases to better understand the behavior of the function.
  • #1
rmcclurk
4
0

Homework Statement



Find limit as z->infinity of exp(z) where z is complex

Homework Equations



See above

The Attempt at a Solution



The solution should be that the limit does not exist, but I don't know why. Any explanations?
 
Physics news on Phys.org
  • #2
Put z=iy, where y is real. Now let y->infinity.
 
  • #3
Is it because e^iy = r(cos(y)+i*sin(y)) and that equation simply oscillates and never goes to infinity no matter how large y gets?
 
  • #4
rmcclurk said:
Is it because e^iy = r(cos(y)+i*sin(y)) and that equation simply oscillates and never goes to infinity no matter how large y gets?

Right, if you put r=1. Or consider z=x and z=(-x) for x real and let x->+infinity. One limit is infinity, and the other is zero. There is no definite single limit as z->infinity. Consider definite cases of z->infinity to get a feeling for what's going on.
 
  • #5
Thanks a lot got it figured out
 

What is the limit of exp(z) as z approaches infinity?

The limit of exp(z) as z approaches infinity is equal to infinity.

What is the limit of exp(z) as z approaches zero?

The limit of exp(z) as z approaches zero is equal to 1.

What is the limit of exp(z) as z approaches a complex number?

The limit of exp(z) as z approaches a complex number is equal to the value of exp(z) at that complex number.

What is the relationship between exp(z) and the exponential function?

The exponential function, denoted as e^z, is equivalent to exp(z), where e is the base of the natural logarithm. Both functions have the same limit as z approaches any real or complex number.

How can the limit of exp(z) be used in practical applications?

The limit of exp(z) is often used in mathematical models involving growth or decay, such as in population growth or radioactive decay. It can also be used in signal processing and control systems to model exponential behavior.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
917
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
955
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Back
Top