Question

In the argand diagram, the complex number z is in the fourth quadrant, then $\overline{z}$, $-z$, $\overline{-z}$ are respectively are in quardrants

• A. 1,3,2
• B. 1,2,3
• C. 3,2,1
• D. 2,1,3

Answer 1

The correct option is B 1,2,3

Let $z=x+iy$
As $z$ is in the fourth quadrant, $x>0$ and $y<0$
$\overline{z}=x-iy$
In this case, the real part would be positive and the imaginary part would be positive. Hence, this would lie in the first quadrant.
$-z=-x-iy$
In this case, the real part would be negative and the imaginary part would be positive. Hence this would lie in the second quadrant.
$\overline{-z}=-x+iy$
In this case, the real part would be negative and the imaginary part would also be negative. Hence, this would lie in the third quadrant.