Let $\omega $ be a complex number such that 2$\omega $ + 1 = z where z = $\sqrt {-3} $. If $$\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k$$, then k is equal to :

Question

Let $\omega $ be a complex number such that 2$\omega $ + 1 = z where z = $\sqrt {-3} $. If

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k$$,

then k is equal to :

-1

-z

Solution

Please login to view the detailed solution steps...

Go to DASH