CVPL2

Deflate $z^3+(2-i)z^2-2iz\,$

$= z\left( z^2 + (2-i)z - 2i \right)\,$

The roots are $z=0, \frac{-(2-i)\pm \sqrt{(2-i)^2+8i}}{2}\,$

To find $\sqrt{3+4i}\,$ , set up the equation $(a+bi)^2 = 3+4i\,$ to get $\sqrt{3+4i} = 2+i\,$ .

The factored form is $z(z+2)(z-i)\,$