If ` 1/ (m+i n) - (x-iy)/(x+iy) =0, where x,y,m,n` are real and `x+iy!=0 and m+i n!=0`, prove that `m^2+n^2=1`.

If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0

If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

If x^my^n = (x + y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

Let f(x)=x^(m/n) for x in R where m and n are integers , m even and n odd and 0

Let (-2 -1/3 i)^3=(x+iy)/27 (i= sqrt(-1)) where x and y are real numbers then y-x equals

If ((1+i)/(1-i))^(2) - ((1-i)/(1+i))^(2) = x + iy then find (x,y).

If arg(z-1)=arg(z+2i) , then find (x-1):y , where z=x+iy

If x^m\ y^n=1 , prove that (dy)/(dx)=-(m y)/(n x)

If x cos A + y sin A = m and x sin A - y cos A = n, then prove that : x^(2) + y^(2) = m^(2) + n^(2)