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 $\dfrac{5}{2}+i.$