If `(a+ib)(x+iy)=(a^(2)+b^(2))i` , then `(x,y)` is

If x, y, a, b in R, a ne 0 and (a + ib) (x + iy) = (a^(2) + b^(2))i , then (x, y) equals

z=x+iy,z^(1/3)=a-ib,(x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then k is :

If (x+iy)(p+iq)=(x^(2)+y^(2))i, prove that x=q,y=p

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

If z=x+iy,z^((1)/(3))=a-ib and backslash(x)/(a)-(y)/(b)=lambda(a^(2)-b^(2)) then lambda is equal to