jee-main 2014 Q63

jee-main · India · 09apr Complex Numbers Arithmetic Solving Equations for Unknown Complex Numbers

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

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

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