A(z_1) and B(z_2) are two points in the Argan | vedclass

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(D) The condition $\arg \left(\frac{z-z_1}{z-z_2}\right)=0$ or $\pi$ implies that the vectors $(z-z_1)$ and $(z-z_2)$ are collinear.This means that th

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the straight line passing through the points $A$ and $B$

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(D) The condition $\arg \left(\frac{z-z_1}{z-z_2}\right)=0$ or $\pi$ implies that the vectors $(z-z_1)$ and $(z-z_2)$ are collinear.This means that the point $z$ lies on the line passing through the points $z_1$ and $z_2$.Specifically,if $\arg \left(\frac{z-z_1}{z-z_2}\right)=0$,the point $z$ lies on the line outside the segment $\overline{AB}$.If $\arg \left(\frac{z-z_1}{z-z_2}\right)=\pi$,the point $z$ lies on the line segment $\overline{AB}$.Therefore,the locus of $z$ is the straight line passing through the points $A$ and $B$,excluding the segment $\overline{AB}$ for the $0$ case and including it for the $\pi$ case,effectively covering the entire line.

$A(z_1)$ and $B(z_2)$ are two points in the Argand plane. Then,the locus of the complex number $z$ satisfying $\arg \left(\frac{z-z_1}{z-z_2}\right)=0$ or $\pi$ is

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