" (8) "[f&x+iy=sqrt((1+i)/(1-i))" ,prove that "x^(2)+y^(2)z1

If x+iy=sqrt((1+i)/(1-i)), prove that x^(2)+y^(2)=1

If x+iy=(1+2i)/(2+i) prove that x^(2)+y^(2)=1

If x+iy=(2+i)/(2-i) then prove taht x^(2)+y^(2)=1

If x+iy=(1+i)(1+2i)(1+3i) , then x^(2)+y^(2) equals:

If z=x+iy such that the argument of (z-1)/(z+1) is always (pi)/(4). Prove that x^(2)+y^(2)-2y=1

If z=x+iy and |2z-1|=|z-2|," prove that" " " x^(2)+y^(2)=1.

If x+ iy=(1+ 4i)(1+5i) , then (x^(2)+y^(2)) is equal to :

If x+ iy=(1+ 4i)(1+5i) , then (x^(2)+y^(2)) is equal to :

If z_1=x_1+iy_1,z_2=x_2+iy_2 and z_1 = (i(z_2+1))/(z_2-1) , prove that x_1^2+y_1^2-x_1= (x_2^2+y_2^2+2x_2-2y_2+1)/((x_2-1)^2+y_2^2)

If z_1=x_1+iy,z_2=x_2+iy_2 and z_1 = (i(z_2+1))/(z_2-1) , prove that x_1^2+y_1^2-x_1= (x_2^2+y_2^2+2x_2-2y_2+1)/((x_2-1)^2+y_2^2)