Let $\;w(Im\;w \neq 0)\;$ be a complex number.Then the set of all complex numbers z satisfying the equation $\;w - w \overline{w}z=k(1-z)\;$ , for some real number k , is :

Question

$(a)\;\{ z : |z|=1\}\qquad(b)\;\{ z : z=\overline{z}\}\qquad(c)\;\{ z : z \neq1\}\qquad(d)\;\{ z : |z|=1\;,z \neq 1\}$