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If n is an integer then show that (1+i)^...

If n is an integer then show that `(1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos(n pi)/(2)`

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If n is be a positive integer,then (1+i)^(n)+(1-i)^(n)=2^(k)cos((n pi)/(4)), where k is equal to

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Knowledge Check

  • Choose the most appropriate option. If n is an integer, compute the value of the fraction ((1+i)^(n))/((1-i)^(n-2))

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

  • The smallest positive integer n for which (1+i)^(2n)=(1-i))^(2n) , is

    A
    1
    B
    2
    C
    3
    D
    4

  • If n in Z , then (2^(n))/(1+i)^(2n)+(1+i)^(2n)/(2^(n)) is equal to

    A
    0
    B
    2
    C
    `[1+(-1)^(n)]i^(n)`
    D
    1

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    If n is a positive integer show that (n+1)^(2)+(n+2)^(2)+....4n^(2)=(n)/(6)(2n+1)(7n+1)

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

    Find the value of 2^n/((1+i)^(2n))+(1+i)^(2n)/(2^n)

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