Question

If $\omega$ is a cube root of unity, then

Answer 1

If $w$ is a cube root of unity then

A]. $1+w+w^2=0⟹|1+w+w^2|=0$

B]. $w^3+(w^3{)}^2=1+1^2=2$

C]. Since the modulus of the complex number and its conjugate are equal so

$\frac{|a+bw+c{w}^2|}{|a+b{w}^2+cw|}=1$

D]. $1+w^n+w^{2}n=0$ [if $n$ in not a integral multiple of $3$]

$=3$ [if $n$ is integral multiple of $3$]