Find all solutions of the equation $z^4+(-2+2\sqrt{2}i)z^3+(3-4\sqrt{2}i)z^2+(4+10\sqrt{2}i)z-10=0$ Find all solutions of the equation:
$z^4+(-2+2\sqrt{2}i)z^3+(3-4\sqrt{2}i)z^2+(4+10\sqrt{2}i)z-10=0$
I don't have any  other idea than to guess them.

HINT:
You can write the same equation as:
$$(z^2-2z+5)(z^2+2i\sqrt2 z-2)=0$$
Then you can find the roots of each brackets separately...
SOLUTION:
$$z=1-2i$$
$$z = 1+2i$$
$$z = -i\sqrt2$$
