First slide

Geometry of complex numbers

Question

suppose $z_{1}, z_{2}, z_{3}$ represently the vertices $A, B,$ and $C$ respectively of a $∆ A B C$ with centroid at $G .$ If the mid point of AG is the origin, then,

Easy

A

$z_{1} + z_{2} + z_{3} = 0$
B

$2 z_{1} + z_{2} + z_{3} = 0$
C

$z_{1} + z_{2} + 4 z_{3} = 0$
D

$4 z_{1} + z_{2} + z_{3} = 0$

Solution

Affix of $G$ is $\frac{1}{3} (z_{1} + z_{2} + z_{3})$
As origin is the mid-point of AG,
$\begin{array}{l} 0 = \frac{1}{2} [\frac{1}{3} (z_{1} + z_{2} + z_{3}) + z_{1}] \\ \Rightarrow 4 z_{1} + z_{2} + z_{3} = 0 \end{array}$

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