Q213 / 270 · NDA 2012 (Phase 1) · Mathematics

If $z=\bar{z}$, then which one of the following is correct?

  • Correct answer
    A
    The real part of $z$ is zero.
  • B
    The imaginary part of $z$ is zero.
  • C
    the real part of $z$ is equal to imaginary part of $z$.
  • D
    The sum of real and imaginary parts of $z$ is $z$.

Solution

$\begin{aligned} z & =x+y \\ \bar{z} & =x-i y \\ \therefore \quad(x+i y) & =-(x-i y) \\ x+i y & =-x+i y \\ 2 x & =0 \\ \operatorname{Re}(\mathrm{z}) & =0 .\end{aligned}$

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

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