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))
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.

• answer will be option d..
  let a and b be 3..
  ((1+3i)/(3-i))^x
  multiplying numerator and denominator by (3+i)
  ((1+3i)*(3+i))/((3-i)*(3+i))^x
  we get
  on solving we get
  (i)^x
  since x doesnot divide by 4 and is even that means i^x for any value of x wii always equal to -1.
• 11 years agoHelpfull: Yes(7) No(0)
• if y=((1+ai)/(b-i))^x then
  answer will be option d.
• 11 years agoHelpfull: Yes(4) No(1)
• please clarify the question....@ankit
  
• 11 years agoHelpfull: Yes(1) No(1)
• what do u mean by 1ai
• 11 years agoHelpfull: Yes(0) No(1)
• sorry its 1+ai
• 11 years agoHelpfull: Yes(0) No(0)
• From the above calculation we can say that "C" is the required answer.
• 9 years agoHelpfull: Yes(0) No(0)