Norm of a function?

I'm confused about norms. I have

1)

2)

How does one get from 1) to 2)? What kind of norm would this be? (i is imaginary number)

Quote:

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Originally Posted by Jason Bourne

I'm confused about norms. I have

1)

2)

How does one get from 1) to 2)? What kind of norm would this be? (i is imaginary number)

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First, note the correction above.

It is the case that for any complex number

Also note than many textbooks use instead of .