If the conjugate of (x+i y)(1-2 i) is 1+i , then

Step-by-step solution

Let z=(x+i y)(1-2 i)=x+i y-2 x i-2 i² y=x+i y-2 x i+2 y z z=x+2 y+i(y-2 x) z = x +2 y - i ( y -2 x ) According to the question, gathered z =1+ i x +2 y - i ( y -2 x )=1+ i gathered On equating the real and imaginary parts from both sides, we get and aligned &x+2 y=1 &y-2 x=-1 aligned 2 x+4 y=2 On adding Eqs. (i) and (ii), we get 5 y=1 y= 1 5 From Eq. (i), we get aligned &2 x +4 ( 1 5 )=2 & 2 x =2- 4 5 & 2 x = 6 5 x = 3 5 & Taking z = x + iy = 1- i 1-2 i 1+2 i 1+2 i &= 1+2 i - i -2 i ² 1-4 i ² & z=(x+i y)(1-2 i)=x+i