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if i=sqrt-1, the number of values of i^n...

if `i=sqrt-1`, the number of values of `i^n+i^-n` for different `n epsilon I`, is:

A

`(2^n)/((1-i)^(2n))+((1+i)^(2n))/(2^n)`

B

`((1+i)^(2n))/(2^n)+((1-i)^(2n))/2^n`

C

`((1+i)^(2n))/(2^n)+(2^n)/(1-i)^(2n)`

D

`(2^n)/((1+i)^(2n))+2^n/((1-i)^(2n))`

Text Solution

Verified by Experts

The correct Answer is:
B,D
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Knowledge Check

  • If i=sqrt(-1) , then {i^(n)+i^(-n), n in Z} is equal to

    A
    `{0,2}`
    B
    `{0,-2}`
    C
    `{0,-2,2}`
    D
    `{0,-2i}`

  • For positive whole number of n, what is the value of i^(4n+1) ?

    A
    A)1
    B
    B)`-1`
    C
    C)i
    D
    D)`-i`

  • The value of 1/(i^n) + 1/(i^(n + 3)) + 1/(i^(n + 2)) + 1/(i^(n + 1)) is :

    A
    `-1`
    B
    `1`
    C
    `0`
    D
    can't be determined

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