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01 Jun 2019, 10:04
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
17% (01:57) correct
83%
(01:52)
wrong
based on 127
sessions
History
Date
Time
Result
Not Attempted Yet
Given that \(i^2\) = −1, for how many integers n is \((n + i)^4\) an integer?
(A) none
(B) 1
(C) 2
(D) 3
(E) 4
(A) none
(B) 1
(C) 2
(D) 3
(E) 4
01 Jun 2019, 10:33
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IMO D ,
it will be integer for 0,1,-1
here ,
((n+i)^2)^2
expand this and put i^2=-1 whereevr you see i^2
after simplifying above expression you will have some part with term i as shown below
n^4-6n^2+1+2ni(n^2-1)
now integer values will depend on the values of n for which the i part becomes zero
such values are 0, 1 and -1
Posted from my mobile device
it will be integer for 0,1,-1
here ,
((n+i)^2)^2
expand this and put i^2=-1 whereevr you see i^2
after simplifying above expression you will have some part with term i as shown below
n^4-6n^2+1+2ni(n^2-1)
now integer values will depend on the values of n for which the i part becomes zero
such values are 0, 1 and -1
Posted from my mobile device
01 Jun 2019, 11:40
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Rubina11
What is the source of this question.
Thanks
Posted from my mobile device
