let Y={(1+ai)/(b-i)}^X where a,b,Xand 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 will always be true(i is a 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 b and a are prime numbers and not equal.
d. both a and b can take any values as long as they are equal

• try all options.
  select test cases for each scenario:
  for each case a),b),c) we consider values for 'a' & 'b' - in each case we get the value of Y as a complex number.
  However when we consider a=b (for both negative and positive values), we always obtain Y as an integer!
  So answer is (d)
• 11 years agoHelpfull: Yes(11) No(0)