If the $$e^{j\omega} = \cos(\omega)+j \sin(\omega)$$ and I have the following equation $$\phi_s = {2\over3}\left(\phi_u+\phi_ve^{{2\pi\over3}j}+\phi_we^{{4\pi\over3}j}\right)e^{-j\theta}$$
The imaginary and real part is the following according the lecture: $$\mathop{\rm Re}(\phi_s)={2\over3}\left(\cos(\theta)\phi_u+\cos\left(\theta-{2\pi\over3}\right)\phi_v+\cos\left(\theta+{2\pi\over3}\right)\phi_w\right)$$ $$\mathop{\rm Im}(\phi_s)={2\over3}\left(\sin(\theta)\phi_u+\sin\left(\theta-{2\pi\over3}\right)\phi_v+\sin\left(\theta+{2\pi\over3}\right)\phi_w\right)$$
According my calculation all the sin
is with a minus. Where do I make the mistake(s)?