If z_1 = 1 + 2i,z_2 = 2 + 3i,and z_3 = 3 + 4i | vedclass

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

Question

(D) Given the complex numbers: $z_1 = 1 + 2i$,$z_2 = 2 + 3i$,and $z_3 = 3 + 4i$. Calculate the distances between the points: $|z_1 - z_2| = |(1-2) + (

Vedclass · Accepted Answer

None of these (Collinear points)

Vedclass · Answer

(D) Given the complex numbers: $z_1 = 1 + 2i$,$z_2 = 2 + 3i$,and $z_3 = 3 + 4i$. Calculate the distances between the points: $|z_1 - z_2| = |(1-2) + (2-3)i| = |-1 - i| = \sqrt{(-1)^2 + (-1)^2} = \sqrt{2}$. $|z_2 - z_3| = |(2-3) + (3-4)i| = |-1 - i| = \sqrt{(-1)^2 + (-1)^2} = \sqrt{2}$. $|z_1 - z_3| = |(1-3) + (2-4)i| = |-2 - 2i| = \sqrt{(-2)^2 + (-2)^2} = \sqrt{8} = 2\sqrt{2}$. Since $|z_1 - z_2| + |z_2 - z_3| = \sqrt{2} + \sqrt{2} = 2\sqrt{2} = |z_1 - z_3|$,the points are collinear and do not form a triangle. Therefore,the correct option is $D$.

If $z_1 = 1 + 2i$,$z_2 = 2 + 3i$,and $z_3 = 3 + 4i$,then $z_1, z_2, z_3$ represent the vertices of a/an:

Similar Questions

If $A = \{z = x + iy : \text{real part of } \frac{\bar{z}-1}{z-i} = 2\}$,then the locus of the point $P(x, y)$ in the Cartesian plane is:

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

If $a$ and $b$ are the least and the greatest values respectively of $|z_1+z_2|$,where $z_1=12+5i$ and $|z_2|=9$,then $a^2+b^2=$

If $\cos \alpha+4 \cos \beta+9 \cos \gamma=0$ and $\sin \alpha+4 \sin \beta+9 \sin \gamma=0$,then $81 \cos (2 \gamma-2 \alpha)-16 \cos (2 \beta-2 \alpha)=$

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module