Let w (Im w ≠ 0) be a complex number. Then the set of all complex numbers z satisfying the equation w - wz = k(1 - z), for some real number k, is:

let 'w' bea+iband z be′x+iy′a+ib−(a−ib)(x+iy)=k(1−x−iy)a+ib−[ax+ayi−bxi+by]=k(1−x)−ikya+ib−ax−ayi+bxi−by=k(1−x)−kyi(a−ax−by)+i(b−ay+bx)=k(1−x)−kyi.comparing real and imaginary coefficients from both sides.k=(a−ax−by)(1−x),k=(ay−bx−by)a−ax−by1−x=ay−bx−byay−axy−by2=ay−bx−b−ayx+bx2+bx−by2=bx2−bb=by2+bx2x2+y2=1|z|=1