What is the Modulus of the Complex Number exp(√i)?

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Homework Help Overview

The discussion revolves around finding the modulus of the complex number exp(√i). Participants are exploring the implications of the exponential function applied to a complex argument.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the reasoning behind the answer scheme that seemingly disregards the imaginary component of the expression. Questions are raised about the validity of the simplifications made in the answer scheme, particularly concerning the cosine value.

Discussion Status

Some participants have identified potential misunderstandings in their approaches and are reflecting on their reasoning. There is an acknowledgment of a mistake by one participant, indicating a progression in understanding, but no consensus has been reached on the correct interpretation of the problem.

Contextual Notes

Participants are working with the assumption that the modulus of a complex number can be derived from its exponential form, but there is confusion regarding the treatment of the imaginary part in the context of the modulus calculation.

unscientific
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Homework Statement



Find |exp(√i)|.


Homework Equations





The Attempt at a Solution



I scanned my working as attached, it seems ok to me but I don't understand why it's wrong..


The answer scheme ignores the exp(i sin (pi/4) ) part and writes the answer as exp(cos (pi/4)) = exp(1/√2).

Would appreciate any help!
 

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unscientific said:

Homework Statement



Find |exp(√i)|.

Homework Equations



The Attempt at a Solution



I scanned my working as attached, it seems ok to me but I don't understand why it's wrong..

The answer scheme ignores the exp(i sin (pi/4) ) part and writes the answer as exp(cos (pi/4)) = exp(1/√2).

Would appreciate any help!
attachment.php?attachmentid=48368&d=1339770269.jpg


Isn't cos(π/4) = (√2)/2 ?
 
just discovered my mistake! thanks anyway guys :)
 
initially i was wondering why they ignored the complex part, but it works out to become this:
 

Attachments

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sorry for the trouble!
 

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