Q59 / 160 · TS EAMCET 2017 · Mathematics

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

  • A
    $x+i y=1-i$
  • Correct answer
    B
    $x+i y=\frac{1-i}{1-2 i}$
  • C
    $x-i y=\frac{1-i}{1+2 i}$
  • D
    $x-i y=\frac{1-i}{1+i}$

Solution

We have, Conjugate of $(x+i y)(1-2 i)$ is $1+i$. i.e. $\quad(x-i y)(1+2 i)=1+i$ $\Rightarrow \quad x-i y=\frac{1+i}{1+2 i}$ Taking conjugate both sides, we get $$ x+i y=\frac{1-i}{1-2 i} $$

Hence, the correct answer is option: 'B'.

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