Prove that `(a) (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4)`, where n is a positive integer. `(b) (1+isqrt(3))^n+(1-isqrt(3)^n=2^(n

`(1+i)^(n) + (1-i)^(n)`
`=(2)^(n//2){cos.(pi)/(4)+isin +cos.(npi)/(4)-isin(npi)/(4)}`
`= 2^((n)/(2)) 2cos.(npi)/(4) = 2^((n)/(2)+1) cos.(npi)/(2) = (sqrt(2))^(n+2) cos.(npi)/(4)`

Prove that `(a) (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4)`, where n is a positive integer. `(b) (1+isqrt(3))^n+(1-isqrt(3)^n=2^(n+1)cos((npi)/3)`, wher

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