It seems intuitive that multiplying by i should shift the phase of a signal by 90 degrees.

I believe this can be shown to be true using euiler identities.

However, something doesn't make sense.

If I multiply cos(theta) by i -- and plot the result, I don't see the cosine shifted by 90 degrees, instead I get a string of complex numbers which I can't even really plot.

So what obvious thing am I not understanding here?

Thanks!