Resultant of Movements
A straight line arrow from one point to another may summarize the movement of an object. The object itself may follow a curved path between the tail or initial point of the arrow and the head or terminal point. Similarly when a sequence of straight line motions is followed, one after another, the arrow joining the initial point of the first motion to the terminal point of the last motion summarizes or gives the sum or resultant of the intermediate motions. Here is a context and motivation for the head to tail addition of arrows or vectors in navigation.
The straight line path between the start and finish of a sequence of movements (shown as arrows on maps) is called their resultant or sum. The vector from A to M gives an example of a resultant, the net result of a sequence of motions. In this map-based example, the vector from A to M represents the top view of a path a bird could fly if does not represent a possible path of the boat. It could be the path if the land was not there -- raise the water level.
www.whyslopes.com
Complex Numbers
Hint: See the (newest) Complex Number. Starter Lesson. for a simple geometric introduction, then continue with easy consequence below.
The fundamental theorem of algebra and partial fraction decomposition in calculus depend on complex numbers.
Easy Consequences
First Earlier (Old) exposition of complex numbers follows in Z1 to B1 below - read for review or revision .
D1 to D6 after provide a review of vectors.
More on Complex Numbers:
Chapters in Volume 3::
Intro assumes the field properties
of real numbers in place of
deriving them geometrically