[" If "a,b,p,q" are real and "root(3)(a-ib)=p-iq" prove that,"],[root(3)(a+ib)=p+iq]

If a,b,p,q are real and 3sqrt(a-ib)=p-iq" ""prove that" " " 3sqrt(a+ib)=p+iq. '

If a,b,p,q are real and (a-ib)^((1)/(3))=p-iq prove that,(a+ib)^((1)/(3))=p+iq

If root(3)(a+ib) = x + iy, prove that : root(3)(a-ib) = x- iy .

If (x+iy)^(5)=p+iq, then prove that (y+ix)^(5)=q+ip

If (a+ib)^(5)=" p "+" iq ," where " "i=sqrt(-1), prove that (b+ia)^(5)=q+ip.

If p,qr are real and p!=q, then show that the roots of the equation (p-q)x^(2)+5(p+q)x-2(p-q=0 are real and unequal.

If (a+i)^2/(2a-i) = p+iq , prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

If (a+i)^2/(2a-i)=p+iq then prove that p^2+q^2=((a^2+1)^2/(4a^2+1))

If p, q, are real and p ne q then the roots of the equation (p-q) x^(2)+5(p+q) x-2(p-q)=0 are

If (a+i)^2/((2a-i))= p + iq , prove that : p^2+q^2 =(a^2+1)^2 /(4a^2+1) .