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

If x+iy=(a+ib)/(a-ib) prove that x^(2)+y^(2)=1

If x+iy=(a+ib)/(a-ib) prove that x^(2)+y^(2)=1

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

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

If x+iy=(a+ib)/(a-ib) prove that x^2+y^2=1

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

x + iy = (a + ib) / (a-ib), provethat x ^ (2) + y ^ (2) = 1

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

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

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)