This applet shows what adding a complex number does to all points of a set.[br][br]Drag the blue points. [br]The point A is the complex number being added.[br]The checkboxes show or hide different shapes.[br]The vector labeled "move vector" is a copy; move it around to compare before and after points on various figures.
This applet shows the function f(z)=z+a, where a is fixed complex number, and the input is any complex number in the plane.[br][br]In coordinates, a=b+ci and z=x+iy. This function adds a to x and b to y. Geometrically, it translates the point or object by a, considered as a vector in the plane.