The book says:[cos (t) – i[Cos (t) -i

[cos(t)-i*sin (t)[X+i[X+i[x+i[x+i*y]= x*cos (t) + y*sin (t) – i *[X[x[X[x*sin (t) + y*Cost)]

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

X*cos (t) + y*sin (t) – i *[X[x[X[x*sin (t) – y*Cost)]

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).