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))

• Where are the statements?
• 12 years agoHelpfull: Yes(1) No(0)
• 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.
• 9 years agoHelpfull: Yes(1) No(0)
• 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.
• 12 years agoHelpfull: Yes(0) No(0)
• please help to solve this problem
  
• 9 years agoHelpfull: Yes(0) No(0)