value of complex multiplier in DFT/FFT
Using Euler's formula you can see that

$$W_4=e^{-j2\pi/4}=e^{-j\pi/2}=\cos(\pi/2)-j\sin(\pi/2)=-j$$

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

$$(-j)^{4k}=1\\(-j)^{4k+1}=-j\\(-j)^{4k+2}=-1\\(-j)^{4k+3}=j$$