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YOU are better than YOU think. Show yourself how:
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Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Do not leave here without it - Logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
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Caution: Site advice is approximately
correct, for some circumstances, not all. Site How-TOs are logically
developed, but not tried and tested. That leaves room for thought and
refinement.. |
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After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
linear2007 Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Explore collaborative whiteboards from
groupboard, twiddla or
scriblink.
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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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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
Vec & Cmplx No Applet B2 C. Conjugates B3 Pythagoras B4 Distance B5 Rt Triangle Similarity B6 Trig., Functions B7 Dot & Cross Products B8 Cosine Law B9 Exponential & cis fns B10 Easy Trig Identities B11 Set Viewpoint Links: Interactive Maths
First Earlier (Old) exposition of complex numbers follows
in Z1 to B1 below - read for review or revision .
First (Old) Complex No Intro Distributive Law A1 Add Poiints A2 Polar Coords A3 Polar Multiply A4 Complex No.s A5 Real Numbers A6 Law of Signs A7 Key Properties B1 2nd Mult Method C1 Unsigned Coords C2 Signed Coords C3 Set Codification C4 More On Real No.s D1 Arrow Navigation D2 Sum of Motions D3 Addition Method I D4 Addition Method II D5 Addition Method III D6 Coordinate Addition D7 1st Distributive Law D8 2nd Distributive Law D9 3rd Distributive Law
D1 to D6 after provide a review of vectors.
More on Complex Numbers:
Chapters in Volume 3::
19 Logs & Powers
19 Natural Log.
19 Exponential Fn.
20 What's Next
21 Add Vectors
22 Complex #'s
23 Complex #'s
23 Trig Identity
23 Proofs of.
24 Complex Logs etc
This further
Complex Number
Intro assumes the field properties
of real numbers in place of
deriving them geometrically
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