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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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

Similar Questions

If $z, iz$ and $z+iz$ are the vertices of a triangle and if $|z|=4$,then the area (in sq. units) of that triangle is:

If $z$ is a complex number satisfying $|z - 3| \leq 5$,then the range of $|z + 3i|$ is (where $i = \sqrt{-1}$).

The complex numbers $z = x + iy$ which satisfy the equation $\left| \frac{z - 5i}{z + 5i} \right| = 1$ lie on

Vedclass Test Series

Exam Paper Generator

Online Exam Module