If (x+iy)(2-3i)=4i, find x,y where `x,y inR`

If (x+iy)^(1/3)=a+ib , where a,b,x, y in R, show that x/a-y/b=-2(a^2+b^2) .

If x = (3 - i) , y = (2 + i) , find |(x + y + 1)/(x - y + 1)|

Find the values of x and y if : ((1+i)x-2i)/(3+i)+((2-3i)y +i)/(3-i) =i , where i=sqrt(-1)

If (x+iy)^(1//3)=a+ib,"where "i=sqrt(-1),then ((x)/(a)+(y)/(b)) is equal to

If (1-i)/(1+i)=x+iy , then x^2+y^2 is equal to:

If (x + iy)^3 = u + iv , then show that u/x +v/y = 4(x^2 - y^2)

If x^(2)+y^(2)=4 then find the maximum value of (x^(3)+y^(3))/(x+y)

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.