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

Step-by-step solution

Given the conjugate of (x+iy)(1-2i) is 1+i . Let z = (x+iy)(1-2i) . Then z = 1+i . Taking the conjugate on both sides, z = 1+i = 1-i . Thus, (x+iy)(1-2i) = 1-i . Dividing by (1-2i) , we get x+iy = 1-i 1-2i . To simplify, multiply the numerator and denominator by the conjugate of the denominator, which is (1+2i) : x+iy = (1-i)(1+2i) (1-2i)(1+2i) = 1 + 2i - i - 2i^2 1^2 + 2^2 = 1 + i + 2 5 = 3+i 5 = 3 5 + i 1 5 . Comparing real and imaginary parts, x = 3 5 and y = 1 5 . Checking the options, x+iy = 1-i 1-2i matches o