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If n is a positive integer, show that ...

If n is a positive integer, show that
`(1 + i)^(n) + (1 - i)^(n) = 2 ^((n+2)/2) cos ((npi)/4)`.

Answer

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If n is integer then show that (1 + i)^(2n) + (1 - i)^(2n) = 2 ^(n+1) cos . (npi)/2 .

A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^(n)+(1-i)^(n)=2^((n//2)+1).cos""(npi)/(4)

Knowledge Check

  • If n is a positive integer, then (1+i)^n+(1-i)^n=

    A
    `2^((n//2)+1).cos(npi)/(3)`
    B
    `2^((n//2)+1).cos(npi)/(4)`
    C
    `2^((n//2)+1).cos(npi)/(5)`
    D
    `2^((n//2)+1).cos(npi)/(6)`

  • If 'n' is a positive integer, then n.1+ (n-1) . 2+ (n-2). 3+….. + 1.n=

    A
    `(n (n+1) )/(2)`
    B
    `(n (n+1) (n+2) )/( 6)`
    C
    `( (n+1)(n+2))/( 2)`
    D
    `(n(n+1) (2n+1))/(6)`

  • If n is positive integer and (1+i)^(2n)+(1-i)^(2n)=k cos (n pi//2) , then the value of k is

    A
    `2^n`
    B
    `2^(n-1)`
    C
    `2^(n+1)`
    D
    1

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