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 three complex numbers are in $A.P.$,then they lie on

$z=x+iy$ and the point $P$ represents $z$ in the Argand plane. If the amplitude of $\left(\frac{2z-i}{z+2i}\right)$ is $\frac{\pi}{4}$,then the equation of the locus of $P$ is

Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}$,where $z \in \mathbb{C}$,be the equation of a circle with center at $C$. If the area of the triangle,whose vertices are at the points $(0,0)$,$C$,and $(\alpha, 0)$,is $11$ square units,then $\alpha^2$ equals

If for the complex numbers $z$ satisfying $|z-2-2 i| \leq 1$,the maximum value of $|3 i z+6|$ is attained at $a+i b$,then $a+b$ is equal to .... .

Let $S = \{z \in \mathbb{C} - \{i, 2i\} : \frac{z^2 + 8iz - 15}{z^2 - 3iz - 2} \in \mathbb{R} \}$. If $\alpha - \frac{13}{11}i \in S$ and $\alpha \in \mathbb{R} - \{0\}$,then $242\alpha^2$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module