`(x+iy)^(1/3) =(a+ib)` then prove that `(x/a+y/b)=4(a^2-b^2)`

(x+iy)^((1)/(3))=a+ibthenprovethat(x)/(a)+(y)/(b)=4(a^(2)-b^(2))

If (x+iy)^(1/3)=a+ib,x,y,ab in R. Show that (x)/(a)+(y)/(b)=4(a^(2)-b^(2))( ii) (x)/(a)-(y)/(b)=2(a^(2)+b^(2))

If (x+iy)=sqrt((a+ib)/(c+id)) then prove that (x^(2)+y^(2))^(2)=(a^(2)+b^(2))/(c^(2)+d^(2))

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

If ((x+i)^(2))/(3x+2)=a+ib, then prove that ((x^(2)+1)^(2))/((3x+2)^(2))=a^(2)+b^(2)

if (1+i x/a) (1+i x/b)(1+i x/c)…=A+iB then prove that (1+ x^2/a^2)(1+x^2/b^2)(1+x^2/c^2)…=A^2+B^2

If x-iy=sqrt((a-ib)/(c-id)) then prove that x^(2)+y^(2)=(a^(2)+b^(2))/(c^(2)+d^(2))

a^(x)=b^(y)=c^(z) and b^(2)=ac then prove that (1)/(x)+(1)/(z)=(2)/(y)

If sqrt(a+ib)=x+iy then prove that sqrt(a-ib)=x-iy