Answer to Question #262537 in Complex Analysis for luka

Question

 Consider the four points ABC , , and D , on a complex plane with affixes 2 - 3i , 1/2 , 1+ 4i and 4 + 2i respectively.

a) Plot these points on complex plane

b) Calculate the affixes of vectors AB and BC

c) Determine the affix of point E such that ABCE is a parallelogram

Answer 1

a)

b)

$$\overrightarrow{AB}=\dfrac{1}{2}-2+(0-(-3))i$$

$$\overrightarrow{AB}=-\dfrac{3}{2}+3i$$

$$\overrightarrow{BC}=1-\dfrac{1}{2}+(4-0)i$$

$$\overrightarrow{BC}=\dfrac{1}{2}+4i$$

c)

$$\overrightarrow{AB}=-\dfrac{3}{2}+3i=\overrightarrow{EC}$$

$$\overrightarrow{BC}=\dfrac{1}{2}+4i=\overrightarrow{AE}$$

$$\overrightarrow{EC}=1-x_E+(4-y_E)i=-\dfrac{3}{2}+3i$$

$$x_E=\dfrac{5}{2}, y_E=1$$

The affix of point E is $\dfrac{5}{2}+i.$