Number of ordered pairs `(s)`, `(a,b)` of real numbers such that `(a+ib)^(2008)=a-ib` holds good is

If 2^(a)=7^(b) then number of ordered pairs (a,b) of real numbers is

If the number of ordered pairs (a,b) where a,b in R such that (a+ib)^(5015)=(a-ib)^(3) is k , then the unit digit of k is equal to________

If the number of ordered pairs (a,b) where a,b in R such that (a+ib)^(5015)=(a-ib)^(3) is k , then the unit digit of k is equal to________

If x, y, a, b are real numbers such that (x+iy)^(1//5)=a + ib and p = (x)/(a) - (y)/(b) , then

If (x+iy)^((1)/(3))=a+ib where x,y,a,b are real numbers such that (x)/(a)-(y)/(b)=k(a^(2)+b^(2)) then the value of k is

the number of real values of x for which the equality holds good |3x^(2)+12x+6|=5x+16 holds good is

The condition for the cube of a+ib to be a real number is:

The condition for the cube of a+ ib to be a real number is