jee-main 2019 Q62

jee-main · India · session1_10jan_shift2 Complex Numbers Arithmetic Trigonometric/Polar Form and De Moivre's Theorem

Let $z = \left( \frac { \sqrt { 3 } } { 2 } + \frac { i } { 2 } \right) ^ { 5 } + \left( \frac { \sqrt { 3 } } { 2 } - \frac { i } { 2 } \right) ^ { 5 }$. If $R ( z )$ and $I ( z )$ respectively denote the real and imaginary parts of $z$, then
(1) $I ( z ) = 0$
(2) $R ( z ) < 0$ and $I ( z ) > 0$
(3) $R ( z ) > 0$ and $I ( z ) > 0$
(4) $R ( z ) = - 3$

Let $z = \left( \frac { \sqrt { 3 } } { 2 } + \frac { i } { 2 } \right) ^ { 5 } + \left( \frac { \sqrt { 3 } } { 2 } - \frac { i } { 2 } \right) ^ { 5 }$. If $R ( z )$ and $I ( z )$ respectively denote the real and imaginary parts of $z$, then\\
(1) $I ( z ) = 0$\\
(2) $R ( z ) < 0$ and $I ( z ) > 0$\\
(3) $R ( z ) > 0$ and $I ( z ) > 0$\\
(4) $R ( z ) = - 3$

Paper Questions

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