Answer
See plot and explanations.
Work Step by Step
Step 1. Let $z=1=cos0+i\ sin0$; we have the fourth roots as $z_k=\sqrt[4] 1(cos\frac{2k\pi+0}{4}+i\ sin\frac{2k\pi+0}{4} )=cos\frac{k\pi}{2}+i\ sin\frac{k\pi}{2} $, where $k=0,1,2,3$
Step 2. For $k=0$, we have $z_0=1$
Step 3. For $k=1$, we have $z_1=cos\frac{\pi}{2}+i\ sin\frac{\pi}{2}=i $
Step 4. For $k=2$, we have $z_2=cos\frac{2\pi}{2}+i\ sin\frac2{\pi}{2}=-1$
Step 5. For $k=3$, we have $z_3=cos\frac{3\pi}{2}+i\ sin\frac{3\pi}{2}=-i $
Step 6. We can plot the above root as shown in the figure.
