How can the polar form of a complex number be$ r(\cos(x)-i\sin(x))$?

Question

I don't understand how this can form can work: $r(\cos(x)-i\sin(x))$. I saw it in my textbook. Surely there should be a "$+$" rather than a "$-$" between the $\cos$ and the $\sin$. If the imaginary part was negative then surely that would be accounted for by the argument which in this case I have written as "$x$".

Answer 1

Perhaps you could use the fact that $-\sin (x) = \sin (-x)$ and $\cos (x) = \cos (-x)$, then your expression becomes $r(\cos (-x) + i \sin (-x))$.