Q138 / 200 · AP EAMCET 2001 · Mathematics

If $\left|\begin{array}{cc}1-i & i \\ 1+2 i & -i\end{array}\right|=x+i y$, then $x$ is equal to

  • A
    $-2$
  • B
    $-1$
  • Correct answer
    C
    $1$
  • D
    $2$

Solution

We have, $\begin{aligned} & \left|\begin{array}{cc}1-i & i \\ 1+2 i & -i\end{array}\right|=x+i y \\ & \Rightarrow \quad-i-1-i+2=x+i y \\ & 1-2 i=x+i y \\ & \Rightarrow \quad x=1, y=-2 \\ & \end{aligned}$

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

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