Latest self Aptitude Question SOLUTION: let y=((1+ai)/(b-i))^x,where a,b,x and y are integers.it is known that x is an even number greater than 100 but not divisible by 4,which of the following statements willl always be

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(#M40010525) SELF question Keep an EYE

let y=((1+ai)/(b-i))^x,where a,b,x and y are integers.it is known that x is an even number greater than 100 but not divisible by 4,which of the following statements willl always be true??(i is complex such that i^2=(-1))

deepika (12 years ago)

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Jamil Ahmed  (12 years ago)

Where are the statements?

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tapesh  (9 years ago)

d.both a and b can take any values as long as they are equal.

y=((1+ai)/(b-i))^x
=(1/(i)^x)*((-i+a)/(b-i))^x ---------->eqn 1 (take i common from (1+ai)^x)
now since x=2n>100 and not equal to 4m.
so let, x=2n
then, 1/(i)^x = (1/(i^2))^n
= (-1)^n
=k (k is either +1 or -1 doesn't matter since it is integr ) (just for writing simplicity)
Now in eqn 1,
y= k*((-i+a)/(b-i))^x ------------>eqn 2
in second part of our equation 2 multiply both numerator and denominator by (b+i)
i.e.
y= k*( ((b-a)i-1-ab) / (b+1) )^x
Now, for y to be integer b-a must equal to zero.

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deepika  (12 years ago)

im sorry,
a.both a and b are positive but not equal
b.both a and b are negative and not equal
c.both a and b are prime numbers and not equal
d.both a and b can take any values as long as they are equal.

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Rajat Sood  (9 years ago)

please help to solve this problem

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