Points, vectors and complex numbers

### 26.1.1 Points, vectors and complex numbers

A point in the Cartesian plane is described with an ordered pair (a,b). It has x-coordinate (abscissa) a and y-coordinate (ordinate) b.

A vector from one point (a1,b1) to another (a2,b2) has associated ordered pair (a2−a1,b2−b1); so the abscissa is a2−a1 and the ordinate is b2−b1.

A complex number a+ib can be associated with the point (a,b) in the Cartesian plane. The complex number is called the affix of the point.

A point in Xcas is specified with the point command (see Section 26.5.2), which takes as argument either two real numbers a,b or a complex number a+ib. In this chapter, when a command take a point as an argument, the point can either be the result of the point command or simply a complex number.

An interactive graphic screen opens whenever a geometric object is drawn, or with the command Alt+G. The objects on the screen can also be created and manipulated with the mouse.

As an example (to be explained in more detail later), the triangle command draws a triangle; the result will be a graphics screen containing axes, the triangle and a control panel on the right.

triangle(1+i/2,2+i,1/2+2i)