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

If the harmonic mean between roots of (5+sqrt(2))x^2-b x+8+2sqrt(5)=0i s4 , then find the value of bdot

Evaluate the following : (i) int sqrt(4 - x^2) dx " " (ii) int sqrt(25 x^2 - 9)dx " " (iii) int sqrt(x^2 + x + 1) dx .

If I=int sqrt((5-x)/(2+x)) dx, then equal

If x, y, z are in A.P then 1/(sqrt(x) + sqrt(y)) , 1/(sqrt(z) + sqrt(x)) , 1/(sqrt(y) + sqrt(z)) are in

If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

If f(x , y) satisfies the equation 1+4x-x^2=sqrt(9sec^2y+4cos e c^2y) then find the value of xa n dtan^2ydot

If side vec A B of an equilateral trangle A B C lying in the x-y plane 3 hat i , then side vec C B can be -3/2( hat i-sqrt(3) hat j) b. -3/2( hat i-sqrt(3) hat j) c. -3/2( hat i+sqrt(3) hat j) d. 3/2( hat i+sqrt(3) hat j)