`(x+iy)^(1/3) =(a+ib)` then prove that `(x/a+y/b)=4(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 (x+i y)^(1//3)=a+i b ,x ,y ,a b in Rdot Show that x/a+y/b=4(a^2-b^2) (ii) x/a-y/b=2(a^2+b^2)

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

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 sin^-1 (x/a) +sin^-1 (y/b) = sin^-1 (c^2/(ab)) then prove that b^2x^2 +2xysqrt(a^2b^2-c^2) = c^4-a^2y^2-2x^2y^2

If (a^(2) + b^(2)) (x^(2) + y^(2)) = (ax + by)^(2) , prove that : (a)/(x) = (b)/(y) .

if 3/(2+cos theta+i sin theta)=a+ib then prove that a^2+b^2=4a-3

If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha

If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha

If x=asintheta and y=btantheta, then prove that (a^2)/(x^2)-(b^2)/(y^2)=1