Suppose, z1 = 0.1 + 0.5i and z2 = 0.1 - 0.5i are from in a unit circle.
How can I find a polynomial of the form $z^2 - az -b$ from (z - z1)*(z - z2)
z1 = 0.1 + 0.5i; z2 = 0.1 - 0.5i ; Expand[(z-z1)(z-z2)]
It gave the folowing output in Mathematica7
$0.01+0. i-0.25 i^2-0.2 z+0. i z+z^2$
$-0.25 i^2+z^2-0.2 z+0.01$