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

IF [x^p y^q = (x+ y)^(p+q)] , prove that dy/dx = y/x.

If x^p . y^q = (x + y)^(p + q) , show that (dy)/(dx) = y/x

If (a+i)^2/((2a-i))= p + iq , prove that : p^2+q^2 =(a^2+1)^2 /(4a^2+1) .

If the normals at four points P (x_i y_i), i = 1, 2, 3, 4 on the rectangular hyperbola xy = c^2 , meet at the point Q(h, k), then prove that x_1 + x_2 + x_3 + x_4 =h

Let N^m be the set of al ordered m-tuples of natral numbers. If x = (x_1.x_2……x_m) y = ( y_1,y_2…..y_m) where x_i,y_i, in N, I = 1, 2 ….m and an operation '+' is defined on N^m by x+y = (x_1 + y_1.x_2+y_2,……x_m + y_m) then prove that given operation is commutative as well as associative.

If x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)= ?

If x^p.y^q=(x+y)^(p+q) , show that dy/dx=y/x ;

If cos^-I x = y, then :

Find the values of x and y if : 3x +5iy = 5i .

Find the values of x and y so that the vectors 2 hat i +3 hat j and x hat i + y hat j are equal.