Complex Numbers And Quadratic Equations question 330
Question: If the points $ P_1 $ and $ P_2 $ represent two complex numbers $ z_1 $ and $ z_2 $ , then the point $ P_3 $ represents the number
Options:
A) $ z_1+z_2 $
B) $ z_1-z_2 $
C) $ z_1\times z_2 $
D) $ z_1\div z_2 $
Show Answer
Answer:
Correct Answer: A
Solution:
This is a parallelogram $ OP_1P_2P_3 $ . Then the mid point of $ P_1P_2 $ and $ OP_3 $ are the same. But midpoint of $ P_1P_2 $ is $ ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} ) $ So that the coordinates of $ P_3 $ are $ ( x_1+x_2,y_1+y_2 ) $ Thus the point $ P_3 $ corresponds to sum of the complex number $ z_1 $ and $ z_2 $ . $ {{\overrightarrow{OP}}_3}={{\overrightarrow{OP}}_1}+\overrightarrow{P_1P_3}={{\overrightarrow{OP}}_1}+{{\overrightarrow{OP}}_2}=z_1+z_2 $
BETA
