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

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

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

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

If z=x+iy prove that |\x|+|\y|lesqrt(2)|\z|

y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)] prove tha t dy/dx is (1)/(2sqrt(x(1-x)))

If y=sqrt(x/a)+sqrt(a/x) , prove that 2x y(dy)/(dx)=(x/a-a/x)

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

If a + ib = c + id , then

If a+ib=(x+iy)/(x-iy) prove that a^2+b^2=1 and b/a=(2xy)/(x^2-y^2)