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A : (1+i)^(6)+(1-i)^(6)=0 R : If n is ...

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)`

Text Solution

Verified by Experts

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

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Knowledge Check

  • Assertion (A) : (sqrt3+i)^6+(sqrt3-i)^6=-128 Reason (R) : If n is a positive integer then (sqrt3+i)^n+(sqrt3-i)^n=2^(n+1)cos(npi)/(6)

    A
    Both A and R are true R is correct explanation to A
    B
    Both A and R are true but R is not correct explanation to A
    C
    A is true R is false
    D
    A is false R is true

  • 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
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    D
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