Unitary Operator: Is it Preserving Vector Length?

[asi123]

Homework Statement

Hey guys.

http://img397.imageshack.us/img397/7987/scan0001q.jpg

I have this operator and I need to check if it's Unitary.
I checked the "length of vector preservation test" as you can see in the pic and I came up with that, that it does not keep the length of a vector.
Does that mean that it's not a Unitary operator?

Thanks.

Homework Equations

The Attempt at a Solution

 

[Cyosis]

This doesn't prove anything, because you're not doing your inner product correctly. What is the definition of the standard complex inner product for vectors? Secondly what is the definition of a unitary operator?