part iii)
Now we just have to find the roots of the equation, so lets just use the identity from part i and the product of roots to simultaneously solve for
![](https://latex.codecogs.com/png.latex?\bg_white \beta)
and
![](https://latex.codecogs.com/png.latex?\bg_white \gamma)
.
Product of roots
Now we just sub
![](https://latex.codecogs.com/png.latex?\bg_white \textcircled{1})
into
lets use the quadratic formula
![](https://latex.codecogs.com/png.latex?\bg_white \\\gamma=\frac{2i\pm\sqrt{(-2i)^2-4(4+4i)}}{-2}\\\\\gamma=\frac{2i\pm\sqrt{{12-16i}}}{-2}\\\\\gamma=\frac{2i\pm2\sqrt{{3-4i}}}{-2})
Now we can use the identity that the question gave us
So yeah the vertices of the parallelogram are -2-2i, 2, 2i, -4i