Absolute Exponential Integration

[M. next]

Hello!

What is the integration of the absolute value of e^ix? That is what is ∫|e^ix|^2 equal to? The whole absolute thing got me lost. Thanks in advance.

 

[HallsofIvy]

For any real number x, |e^{ix}|= 1.

 

[M. next]

Can you please explain why? Thank you for your reply.

 

[micromass]

What is the definition of $e^{ix}$? And what is the definition of the $|~~|$?