jee-main 2018 Q62

jee-main · India · 15apr_shift1 Complex Numbers Arithmetic Identifying Real/Imaginary Parts or Components

The set of all $\alpha \in R$, for which $w = \frac { 1 + ( 1 - 8 \alpha ) z } { 1 - z }$ is a purely imaginary number, for all $z \in C$ satisfying $| z | = 1$ and $\operatorname { Re } z \neq 1$, is
(1) $\{ 0 \}$
(2) an empty set
(3) $\left\{ 0 , \frac { 1 } { 4 } , - \frac { 1 } { 4 } \right\}$
(4) equal to $R$

The set of all $\alpha \in R$, for which $w = \frac { 1 + ( 1 - 8 \alpha ) z } { 1 - z }$ is a purely imaginary number, for all $z \in C$ satisfying $| z | = 1$ and $\operatorname { Re } z \neq 1$, is\\
(1) $\{ 0 \}$\\
(2) an empty set\\
(3) $\left\{ 0 , \frac { 1 } { 4 } , - \frac { 1 } { 4 } \right\}$\\
(4) equal to $R$

Paper Questions

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