Question

1) If w is a complex cube root of unity, show
that
i) (2-w)(2-w×w)=7
​please answer me fast

Answer 1

(2-W)(2-W×W)=7

1. let (2-W)(2-W×W) is L.H.S and 7 is R.H.S
2. then solve L.H.S

Answer 2

$(2-\omega)(2-\omega \times \omega)=7$, proved.

Step-by-step explanation:

We have,

$(2-\omega)(2-\omega \times \omega)$

Prove that, $(2-\omega)(2-\omega \times \omega)=7$

L.H.S. $=(2-\omega)(2-\omega \times \omega)$

$=(2-\omega)(2-\omega^{2} )$

$=2(2-\omega^{2} )-\omega(2-\omega^{2} )$

$=4-2\omega^{2} -2\omega+\omega^{3}$

$=4-2(\omega^{2} +\omega)+1$

[ ∵ $\omega^{3}=1$]

$=5-2(-1)$

[ ∵ $1+\omega +\omega^{2}=0$]

$=7$=R.H.S, proved.