I have the following from the question (in the 2D complex coordinate system):

z3 - z1 = r(z2 - z1), where z1, z2, z3 are complex numbers and r is a real number. I have to show that z1, z2 and z3 lie on the same line. In order to solve the rest of the question, it's recommended that

z3 - z1 = r(z2 - z1) should be rewritten in the form Ax + By + C = 0, which I have no idea how to do.

Any help would be greatly appreciated.

Thanks