Roots of unity for beginners -1

The solutions of $x^3 - 1 = 0$ are $x = 1, e^{\frac{2i\pi}{3}}, e^{\frac{4i\pi}{3}} =$ $= 1, \cos \frac{2\pi}{3} + i\sin \frac{2\pi}{3}, \cos \frac {4\pi}{3} + i \sin \frac {4\pi}{3} \Rightarrow$ the product of all the imaginary parts of the no real solutions of $x^3 - 1 = 0$ is $\sin \frac{2\pi}{3} \cdot \sin \frac{4\pi}{3} = \frac{\sqrt{3}}{2} \cdot (- \frac{\sqrt{3}}{2}) = - \frac {3}{4}$

$x^{3}$ -1=0
or, (x-1)( $x^{2}$ +x+1)=0 ...............................(by factorising)
or, x=1 and x= $\frac {-1 +-{\sqrt{1-4}}}{2}\ .....................(by Sridharacharya)$
So imaginary roots are
x= $\frac {-1 +{\sqrt{3}}i}{2}$ and x= $\frac {-1 -{\sqrt{3}}i}{2}$
imaginary parts are $\frac {+{\sqrt{3}}i}{2}$ and $\frac {-{\sqrt{3}}i}{2}$
multiplying them we get ,
= $\boxed{- 0.75 }$