examples – Read a book about complex numbers and understand their result

The book says:[cos (t) – i[Cos (t) -i
[cos(t)-isin (t)[X+i[X+i[x+i[x+iy]= xcos (t) + ysin (t) – i *[X[x[X[xsin (t) + yCost)]

but every time I try to solve the problem according to the rules of complex numbers, I get:

Xcos (t) + ysin (t) – i *[X[x[X[xsin (t) – yCost)]

which differs by a minus sign before the last term.
Am I missing some identity rule or complex number here?
This should be the same as the rotation by a negative angle that would be the answer I got (I think).