Dealing with complex operation in Quantum mechanics (1 Viewer)

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In proving that for the norm to be preserved, U must be unitary. I ran across this:

Re(λ<ø|ψ>)=Re(λ<Uø|Uψ>)

if λ=i, it says that then it follows that Im(<ø|ψ>)=Im(<Uø|Uψ>), how's this? I know that Re(iz)=-Im(z) in complex, but here the inner product <ø|ψ> is not z, or is it?

If you could point out how this took place, I would be thankful!
 
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Yes, <ø|ψ> is a complex number, if that's what you're asking - It's not entirely clear to me.
 
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Yes, thanks. I noticed that after I posted this!!
 

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