Is exp(i.x) with x=-infinity equal to zero?

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SUMMARY

The expression exp(i.x) for x = -infinity is undefined and does not converge to zero or any other value. The modulus of the complex number remains one, and as x approaches negative infinity, the argument of the exponential function leads to an infinite rotation of the unit vector, making the phase indeterminate. Therefore, the function does not yield a meaningful result at infinity, and the concept of convergence does not apply in this context.

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sam2
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Hi all,

Looking for some help on the following problem. Any replies much appreciated.

I have the complex number

exp(i.x)

If x = - infinity,

is this zero?? Is there any intuitive/straightforward value that it should be? I decomposed the expression into cos and sin and it looks like the number doesn't converge to anything!

regards,
 
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Of course it doesn't converge.U need a complex number of different modulus.The one u've chosen has modulus one,i.e. 1.U cannot make it's argument go to infinity,coz that would mean rotating the unit vector (which is represented by e^(ix)) an ininite amount of times and the phase could not be determined.

Daniel.
 
It is undefined, and there is no reason why it should be defined.
 
sam2 said:
Hi all,

Looking for some help on the following problem. Any replies much appreciated.

I have the complex number

exp(i.x)

If x = - infinity,

is this zero?? Is there any intuitive/straightforward value that it should be? I decomposed the expression into cos and sin and it looks like the number doesn't converge to anything!

regards,

Well, it doesn't go to infinity because of the very reason that you quoted. But don't worry : there is NO problem because this function is NOT DEFINED in the infinity. So, there is no problem and why should there be any ?


marlon
 
Got it.

Many thanks for the replies.

Regards,
Sam
 
A comment: a number is a number, it doesn't make sense to say it "converges" to anything. While the distinction is often blurred, it is still important to remember that the concept of limit is different than that of a number.
 
Last edited:

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