If `sqrt(x-iy)=a-ib` and a,b,x,y are real then show that, `sqrt(x+iy)=a+ib.`

If a,b,x,y are real and 3sqrt(x+iy)=a+ib show that , 3sqrt(x-iy)=a-ib

If a,b,x,y are real and 3sqrt(x+iy)=a+ib show that , 3sqrt(x-iy)=a-ib (x)/(a)+(y)/(b)=4(a^(2)-b^(2)).

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

If (x+iy)^((1)/(3))=a+ib where x,y,a,b are real numbers such that (x)/(a)-(y)/(b)=k(a^(2)+b^(2)) then the value of k is

If (x+iy)^(1/3)=a+ib , where a,b,x, y in R, show that x/a-y/b=-2(a^2+b^2) .

If sqrt(x+iy)=+-(a+ib), then find sqrt(-x-iy)

If x, y, a, b are real numbers such that (x+iy)^(1//5)=a + ib and p = (x)/(a) - (y)/(b) , then

If (x - iy) ^(1//3) = a - ib, then show that (x)/(a) + (y)/(b) = 4 ( a ^(2) - b ^(2)).

If a,b,c,d,x,y are real and (a+ib)(c+id)=x+iy, show that , (a-ib)(c-id)=x-iy