If `z = x - iy` and `z'^(1/3) = p +iq,` then `1/(p^2+q^2)(x/p+y/q)` is equal to

If p^(2)+q^(2)=1,p,q in R, then (1+p+iq)/(1+p-iq) is equal to

If z=x-iy,z^((1)/(3))=p+iq then ((x)/(p)+(x)/(q))(p^(2)+q^(2))=

If x^3 + y^3 + z^3 = 3(1 + xyz) , P = y + z - x, Q = z + x - y and R = x + y - z, then what is the value of P^3 + Q^3 + R^3- 3PQR ?

If (p+iq)/(r+is) = x + iy , prove that (p-iq)/(r-is) = x -iy and (p^(2)+q^(2))/(r^(2)+s^(2))=x^(2)+y^(2) ,where p,q,r,s,x,y,inR