# value of complex multiplier in DFT/FFT

I am studying proakis book digital signal processing using matlab 3rd ed

but i am bit confused about calculation of value complex multiplier W

fig is attached. i am not able to understand how the values of W are found/calculated in this fig in red enclosure

how/why we know that W base 4 and raised to the power 1 is equal to -j

$$W_4=e^{-j2\pi/4}=e^{-j\pi/2}=\cos(\pi/2)-j\sin(\pi/2)=-j$$
With $$j^2=-1$$ it should be easy to verify that
$$(-j)^0=(-j)^4=1\quad\text{and}\quad(-j)^2=(-j)^6=-1$$
It's important to develop a geometric intuition which allows you to immediately see these equivalences. Multiplication with $$j$$ corresponds to a rotation by $$\pi/2$$ in the complex plane, and multiplication with $$-j$$ is a rotation by $$-\pi/2$$. So in general for $$k\in\mathbb{Z}$$ you have
$$(-j)^{4k}=1\\(-j)^{4k+1}=-j\\(-j)^{4k+2}=-1\\(-j)^{4k+3}=j$$