Question 979976


Let us introduce complex numbers

x = 6 -  i;

y = 7 + 3i;

u = 8 + 2i;

v = 7 - 2i.


They are vertices of a quadrilateral in the complex plane.


Now,  calculate these differences of complex numbers:

y - z = 1 + 4i,     and

u - v = 1 + 4i.


The difference &nbsp;y-z&nbsp; represents the side &nbsp;<B>zy</B>&nbsp; of the quadrilateral &nbsp;(the segment from the vertex &nbsp;<B>z</B>&nbsp; to the vertex &nbsp;<B>y</B>).


The difference &nbsp;u-v&nbsp; represents the side &nbsp;<B>vu</B>&nbsp; of the quadrilateral &nbsp;(the segment from the vertex &nbsp;<B>v</B>&nbsp; to the vertex &nbsp;<B>u</B>).


As you see, &nbsp;the complex numbers &nbsp;y-z&nbsp; and &nbsp;u-v&nbsp; are equal. 

It means that the corresponding segments are parallel and have the same length. 


Hence, &nbsp;our quadrilateral is a parallelogram. 


See my lessons on complex numbers in this site:

<A HREF=http://www.algebra.com/algebra/homework/complex/Review-of-lessons-on-complex-numbers.lesson>REVIEW of lessons on complex numbers</A>.