Question

If $\omega$ = $\frac{-1+i\sqrt{3}}{2}$ , then $Z_1$ = $\frac{-\sqrt{3}-i}{2}$ and $Z_2$ = $\frac{\sqrt{3}-i}{2}$ can be expressed in terms of $\omega$ and ${\omega }^2$ as

• A. -i , i
• B. i , - i
• C. i , i
• D. -i , -i

Answer 1

The correct option is C

i , i

$\omega$ is a cube root of unity . Then ${\omega }^2$ = $\frac{-1-i\sqrt{3}}{2}$

$Z_1$ = $\frac{-\sqrt{3}-i}{2}$ = i $\frac{-1+i\sqrt{3}}{2}$
= i$\omega$

$Z_2$ = $\frac{\sqrt{3}-i}{2}$ = i $\frac{(-1-i\sqrt{3})}{2}$
= i${\omega }^2$