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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!
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!