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

[unscientific]

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!

 

[SammyS]

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!

Isn't cos(π/4) = (√2)/2 ?

 

[unscientific]

just discovered my mistake! thanks anyway guys :)

 

[unscientific]

initially i was wondering why they ignored the complex part, but it works out to become this:

 

[unscientific]

sorry for the trouble!