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

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

COMEDKCOMEDK 2014Complex Numbers and Quadratic Equations

Solution:

Let $z =a+ ib$ then in III quadrant $a < 0, b < 0$
Its conjugate $\bar{z} = a +ib = a -ib = a+ (-ib)$
= $a + ik $ where $k = -b$
$\Rightarrow \:\: a < 0, k > 0$
$\Rightarrow \:\: \bar{z}$ lies in II quadrant,