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

AI Thread Summary
The discussion revolves around finding the modulus of the complex number exp(√i). The original poster is confused about their solution, particularly regarding the treatment of the exp(i sin(π/4)) term in the answer scheme. They initially believed that the complex part was ignored but later realized that cos(π/4) equals √2/2, clarifying their misunderstanding. Ultimately, they acknowledge their mistake and express gratitude for the assistance. The conversation highlights the importance of understanding the components of complex exponentials in calculations.
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:
 

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sorry for the trouble!
 
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