jee-main 2017 Q61

jee-main · India · 09apr Complex numbers 2 Roots of Unity and Cyclotomic Properties

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt { - 3 }$. If $$\left| \begin{array} { c c c } { 1 } & { 1 } & { 1 } \\ { 1 } & { - \omega ^ { 2 } - 1 } & { \omega ^ { 2 } } \\ { 1 } & { \omega ^ { 2 } } & { \omega ^ { 7 } } \end{array} \right| = 3 k$$ then $k$ is equal to:
(1) $z$
(2) $- z$
(3) $- 1$
(4) 1

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt { - 3 }$. If
$$\left| \begin{array} { c c c } { 1 } & { 1 } & { 1 } \\ { 1 } & { - \omega ^ { 2 } - 1 } & { \omega ^ { 2 } } \\ { 1 } & { \omega ^ { 2 } } & { \omega ^ { 7 } } \end{array} \right| = 3 k$$
then $k$ is equal to:\\
(1) $z$\\
(2) $- z$\\
(3) $- 1$\\
(4) 1

Paper Questions

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