If `sqrt(x+i y)=+-(a+i b),` then find`sqrt( -x-i ydot)`

If sqrt(3)+i=(a+i b)(c+i d) , then find the value of tan^(-1)(b//a)+tan^(-1)(d//c)

If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

If z=sqrt13-sqrt11i , then find zbarz dot

If z=sqrt7-sqrt5i , then find zbarz dot

If z=sqrt3-sqrt2i , then find zbarz dot

If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

If z=sqrt12-sqrt7i , then find zbarz dot

If y=sqrt((a-x)(x-b))-(a-b)tan^-1sqrt((a-x)/(x-b)) ,show that dy/dx=sqrt((a-x)/(x-b))

If (sqrt(a + 2b) + sqrt(a - 2b))/(sqrt(a + 2b) - sqrt(a - 2b)) = sqrt3 and a^(2) + b^(2) = 1 , then the find values of a and b. (b) If sqrt((x - sqrt(a^(2) - b^(2)))^(2) + y^(2)) + sqrt((x + sqrt(a^(2) - b^(2)))^(2) + y^(2)) = 2a then prove that (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1

If sqrt(x) + sqrt(y)=4, f i n d (dx/dy) a t (y = 1).