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# Number of integral values of n for which the quantity (n+i)^4 where i^2=-1, is an integer is (A) 1      (B) 2          (C) 3               (D) 4

Aman Bansal
592 Points
8 years ago

Daer Tanayraj,

Total 3 integral solutions are possible.

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Aman Bansal

Vikas TU
14149 Points
8 years ago

(n+i)^4 = I

(n+i) (n+i)3 = I

(n+i) (n- i + 3n2i - 3n)  = I

n4 - ni +3n3i - 3n2 + in3 + 1 - 3n2 - 3ni = I

(n4 - 6n2 + 1) + i(4n- 4n) = I +i(0)

a) n4 - 6n2 + 1 = 0

n = no solution.

no integer.

b)  4n- 4n = 0

n(n2 - 1) = 0

n = 0

n = 1

n = -1

Hence (b) 2 integers are possible as 0 is not considered as an ineteger.

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