Question 1207264
<pre>

This is a piecewise graph with parameter t.

{{{"z(t)"}}}{{{""=""}}}{{{system(

matrix(2,3,

t-i*t,for, 0<=t<=2,
t-i, for, 2<t<=4))}}}

We will use a two-dimensional Cartesian plane, and identify the 
point with coordinates (x,y) with the complex number z = x+iy. 
Here, 'i' is the imaginary unit and is identified with the point 
with coordinates (0,1).

We normally think of an "arc" as a curved line.  However in complex
analysis we use a more general definition. A set of points in the 
complex plane is called "an arc" if x = x(t) and y = y(t) for a<u><</u>t<u><</u>b 
where x(t) and y(t) are continuous functions of real parameter t. 
We denote an arc C as z(t)=x(t)+iy(t) for a<u><</u>t</u><u><</u>b.

The left part of the graph where t goes from t=0 to t=2,
is a line segment from 0-i*0, or the point (0,0) to 2-i*2, or the 
point (2,-2), where the segment includes both its endpoints.

{{{drawing(400,400,-5,5,-5,5,
graph(400,400,-5,5,-5,5), line(0,0,2,-2),

circle(2,-2,.1),circle(2,-2,.05),circle(2,-2,.075),
  
circle(0,0,.1),circle(0,0,.05),circle(0,0,.075)


)}}} 

The right part of the graph where t goes from t=2 to t=4,
is a line segment from 2-i, or the point (2,-1) to 4-i, or 
the point (4,-1), where the segment does not include its 
left endpoint, but does include its right endpoint.

{{{drawing(400,400,-5,5,-5,5,
graph(400,400,-5,5,-5,5), line(0,0,2,-2),

circle(2,-2,.1),circle(2,-2,.05),circle(2,-2,.075),
  
circle(0,0,.1),circle(0,0,.05),circle(0,0,.075),



line(2.13,-1,4,-1),

circle(4,-1,.1),circle(4,-1,.05),circle(4,-1,.075),
  
circle(2,-1,.1)



)}}} 

Edwin</pre>