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

If n is a positive integer, show that
`( P + iQ)^(1//n) + ( P - iQ)^(1//n) = 2 ( P^(2) + Q^(2))^(1//2n) cos (1/n , tan . Q/P)`.

Text Solution

Verified by Experts

The correct Answer is:
`2 (P^(2) + Q^(2) )^(1//2n) cos [ (1)/(n) tan^(-1)"" (Q)/(P) ]`
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Knowledge Check

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

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