Q72 / 180 · COMEDK 2014 · Mathematics

If a complex number lies in the III quadrant. Find the quadrant in which its conjugate lies.

  • A
    I quadrant
  • Correct answer
    B
    II quadrant
  • C
    III quadrant
  • D
    IV quadrant

Solution

Let $z=a+i b$ Then, in third quadrant $a < 0, b < 0$. Its conjugate $\bar{z}=\overline{a+i b}=a-i b=a+(-i b)$ $=a+i k$, where $k=-b$ $\Rightarrow \quad a < 0, k>0$ $\Rightarrow \quad \bar{z}$ lies in II quadrant.

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

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