Evaluate the following: `x^6+x^4+x^2+1,\ w h e n\ x=(1+i)/(sqrt(2))`

Explanation

Given:`x=(1+i)/(sqrt(2))`

Then we have to find
`x^6+x^4+x^2+1`

So,

`x^6+x^4+x^2+1=((1+i)/(sqrt(2)))^6+((1+i)/(sqrt(2)))^4+((1+i)/(sqrt(2)))^2+1`

`x^6+x^4+x^2+1=(((1+i)^6)+(2(1+i)^4)+(4(1+i)^2)+((sqrt(2))^6))/((sqrt(2))^6)`

Since `(i^2)=-1`

`x^6+x^4+x^2+1=((1+i)^4(1^2+(i^2)+2i)+2((1)^2+(i^2)+2i)((1)^2+(i^2)+2i)+4((1)^2+(i^2)+2i)+(sqrt(2))^6)/8`

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