# 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
9 years ago

Daer Tanayraj,

Total 3 integral solutions are possible.

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple  to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Vikas TU
14149 Points
9 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.

PLZ  APPROVE!