Solve Equation

walrein_lim88

antimatter

Has an imaginary root => there should be a factor of (z-ri) where r is the root that yet determined and i is sqrt(-1). The conjugate of the imaginary root is also a root for the equation, => (z+ri) is another factor of the equation. Therefore, we should be able to factor out (z^2+r^2). Dividing the equation with (z2+r2) and then setting the remainder =0, we get something like r4+kr2=45. I think every real value of r and k statisfying this equation are the answer, but here i think we don't know which r and k is the answer. In principle, once we get the value of r and k, the other roots can be found from the result of the division, z2-2z+k+r2=0.