On Page 30 in the Art Of Electronics (2nd Edition).
The two images below describe the conservation of Sinusoidal signals to a complex representation and back. I am perfectly ok with the first image. The next image has me stumped.
In particular, I am stumped at the description of V(t) and I(t)
For V(t), I understand why they say V(t) = Re(V * e^jwt)
I do not understand the next line of the simplification V(t) = Re(V)cos(wt) - Im(V) sin(wt)
e^jwt should simplify to
cos(wt) + jsim(wt), I don't understand how V is distributed to the second equation.
I guess I(t) would follow similarly. Can someone help with the factoring?