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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

enter image description here

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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

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

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