Question

If $\omega$ is a cube root of unity, then find the conjugate of $2\omega -3i$

Answer 1

We know that,

$\omega =\frac{-1+i\sqrt{3}}{2}$

$⟹2\omega =-1+i\sqrt{3}$

$⟹2\omega -3i=-1+i\sqrt{3}-3i$

$⟹2\omega -3i=-1+i(\sqrt{3}-3)$

$\therefore$ Conjugate of $2\omega -3i=-1-i(\sqrt{3}-3)$