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 , y are real and x + iy=0 then

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^(4)+2x.i )-(3x^(2)-iy)=(3-5i)+(1+2iy) then find the real value of x and y.

If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y) , show that : x + y + 2 = 0.

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

Prove that, |x-iy|/|-x+iy|=1

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

If m, n integers and x = cos alpha + i sin alpha , y = cos beta + i sin beta, then prove that x^(m) y^(n) + 1/(x^(m)y^(n)) = 2 cos ( m alpha + n beta) " and " x^(m) y^(n) - 1/(x^(m) y^(n)) = 2 i sin ( m alpha + n beta) .

If x_(n) + iy_(n) = (1 + i)^(n) then x_(n - 1) y_(n) - x_(n) y_(n- 1) =