Head-To-Tail Method
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. That is a context and motivation for the head to tail addition of a sequence of arrows or vectors in navigation.
When two movements or motions, one after another, are summarized by arrows with the head of the first, its terminal point, at the tail of the second, the second's initial point, the sum or resultant of these two movements, vectors or arrows is summarized by the the arrow joining the initial point of the first motion to the terminal point of the second. This describes the head-to-tail method of adding two arrows or vectors together. The head of the first must be at the tail of the second. Here is a context and motivation for the head to tail addition of a sequence of arrows or vectors in navigation, a special case of the previous lesson.
Head to Tail Addition Method
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Complex Numbers |
The fundamental theorem of algebra and partial fraction decomposition in calculus depend on complex numbers.
Easy Consequences
Hint: See the (newest) Complex
Number. Starter Lesson.
for a simple geometric introduction, then continue with easy consequence below.
The clearest geometric proof of the distributive law appears in the
folder.
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