Should I Shift by 1 or 4? Understanding Fourier Transform Time Shift

[EvLer]

I am given this signal:
x(t) = sin(4(t-1))
and I need to find X(jw), i.e. it's FT, so I am confused whether I shift by 1 or by 4, in other words whether I multiply F{sin(4t)} by e^(4jw) or by e^(1jw)

which one is it? I am thinking it's 4jw... is it right?

 

[HallsofIvy]

Aarg! Those engineers and their jmaginary numbers!

I hope you will bear with me as I use "i" rather than "j". I just can't force myself to that heresy.

sin(4(t-1))= sin(4t- 4). Looks to me like you need to shift by 4.

 

[EvLer]

Aarg! Those engineers and their jmaginary numbers!

thanks

 

[EvLer]

a bit off topic

perhaps i should have started a different thread, but since HallsofIvy has mentioned, i couldn't help but ask: is there any tiniest difference between i and j, i.e. are we, engineers, underestimate imaginary numbers in some way?
It always comes up and i just would like to satisfy my curiosity.

 

[bhupala]

Mr EvLer,

There is no big deal in taking j instead of i for imaginary numbers. For engineers, 'i' represents current. To avoid confusion engineers take 'j' for imaginary part.