Question

show that (1-omega+omega ²)⁶ + (1+omega-omega²)⁶=128​

Answer 1

Answer:

Given:

The equation is,

(1-omega+omega ²)⁶+(1+omega-omega²)⁶=128

(1-w+w²)⁶+(1+w-w²)⁶=128

Formula used:

As we know that,

• 1+w+w²=0
• w³=1

Solution:

Take LHS,

→ (1-w+w²)⁶+(1+w-w²)⁶

→ ((1+w²)-w)⁶+((1+w)-w²)⁶

→ (-w-w)⁶+(-w²-w²)⁶

→ (-2w)⁶+(-2w²)⁶

→ (2)⁶(w⁶+w¹²)

→ (2⁶)(w⁶)(1+w⁶)

→ 64((1+(w³)²)

→ 64(1+1)

→ 64(2)

→ 128

So, (1-w+w²)⁶+(1+w-w²)⁶=128.