Straight line in complex plane

Slope of a straight line in complex form

Equation of a straight line on the complex plane passing through a point P denoting the complex number alpha and perpendicular to the vector vec OP where ' O' is the origin can be written as

Prove that the points represented by the roots of the equation z^(2)=(1+z)^(4) the straight line.Find the complex equation of the straight line.