- Complex Math
- Independent Axis
- Fine Tuning Time Space
- Four Dimensional Space
- Graphs
- Multiplication
- The Definition of i
- Construction of the i distribution
- Transformations
- Geometry of i
- Commentary
- Art
- Ln(x)
- Time Clock
- Probabilities
- Analysis of the Normal Curve
- Prime Numbers
- Null Set
- Complex Trigonometry
- The Four Subspaces

# Complex Math

- Author:
- RV'SMath

- Topic:
- Complex Numbers

06/12/2020 I deleted "equations in x" because I made a mistake and had each number f(x) off by 1 place. It is an easy fix but I took it down until I correct the mistake.
04/16/20 - On "Integral Ln x" by accident I left out the "number 2" in the denominator in line 2 on the right hand side, I believe, when showing 1 = xt.
12-30-2018 - Correction - I found that in the "Vector Addition" worksheet there is a "Dimension Leader Line" that needs to be - moved - so it's "dimension" is equal to " 1." It's labeled; " i " and should be relocated so the corresponding math above is understandable and applicable to the drawing itself.
09-14-2018 - After inspecting my ' time clocks ' they seem to be off about 1 sec. from being at 20 sec. per cycle.
11-18-2017 This book is made for observation purposes only or something only to consider as relationships of numbers. Applied Math
03-01-2017 Today I made some changes to two worksheets involving the " a " vectors in the (1,-1) position. Their lengths were supposed to be governed by the slider " a " dimension which I had mistakenly made the " Square root of " a " " which is now corrected. It is easy to hastily make these mistakes while trying to build this idea. Sorry for any confusion this may have caused.
09-28-2016 - I made some changes to some worksheets. When I find that I made mistakes I try to fix them.
08-17-2016 - In drawing this relationship of Triangle in this manner it must be said that the 1st quadrant has technically a 2:1 scale as opposed to below the axis which is 1to1; consequently when drawing the vectors it will look different than what I had drawn on a blank page. Theoretically though, my point to drawing this triangle in this manner was in fact to set all elements equal to each other and then determine their dimension or relationship; the math is proportional to itself so as long as you keep the relationships of "a" you will get the same results. I really did not notice that this would create such a big problem! I did a lot of different versions of this relationship and that is why it is called "Independent Axis" so long as you keep the relationships proportional to each other which "scale" may not be so apparent to the viewer but is common amongst drafters which I incorporated drafting into the idea of math. Again this math was not supposed to replace common math ideas but is experimental. You can see the relationship in my Complex Trigonometry Worksheet.
Today's Date 07-01-2016
My Approximation for Pi ≈ 1.35 + 1.41 + .24 + √ 8/ 20 = 3.14142135.... - Also see the "Box Function" in Chapter Ln(x). The Null Set is important too.
The applications Chapters are Ch. 1 and Ch.13 through Ch. 18 - Show this relationship at work. The other Chapters primarily show geometry which takes time to look at.
2 - 29 - 2016 ( See i - pairs where I show the Null Set:{-1,1,0,i,i²} graphically. ) - I was looking at the 'Step Function' again and that thing is pretty cool: See 'Four Dimensional Space.'
2 - 21 - 2016: I updated the worksheet - Complex Geometry - Time Motion to show the velocity vector in action.
2 - 19 - 2016 I Expanded my Complex Trigonometry Grid to Have reference equations as ' Units' for the Grid- which give location reference on the Grid itself.
2 - 6 - 2016; This math is ' experimental ' geometrical relationships, that I hope supports my Hypothesis in the work sheet; ' Independent Axis. '
(This math is not meant to be a contradiction to traditional mathematics; My math is applied mathematics with specific ideas that I use for the basis of the geometries.)
On the other hand.
(I do hope; that both my books on applied math - can be applied to traditional mathematics, with the hope of helping solve some traditional math problems?)
1 - 31 - 2016: I updated Complex Trigonometry Worksheet - Incorporated a "Time" Grid.
a) I Removed my "Time Equation": After looking at the functioning of the equation; it needs to be reconfigured; It must be an Increasing Function!
1 - 30 - 2016: http://www.space.com/31765-ancient-babylonians-tracked-jupiter-with-math.html - See Story and Compare to Complex Trigonometry - I added two versions
of worksheets, using this relationship, and i - geometry. 1 - 31 - 2016: ( I made a correction to Worksheet; Time(i) space time of "a")
1- 17 - 2016 - I removed the " Complex Trigonometry " work sheet - I need to look at that more closely.
1 - 18 -2016 - ( I moved this to its' own chapter - I clarified the Geometry and the Problem I stated above )
1 - 11 - 2016
i geometry dimensions ; a = 1 - Shows how the Geometry fits in perfectly with a circle of diameter 4.
10 - 18 - 2015 - Prime Numbers - The Complete Solution Generates prime number values - I listed some in left bottom column of page
http://news.yahoo.com/math-could-reveal-hidden-sources-chaos-125023192.html - ( Some really good geometry is shown in " Center Line e(x) " )
http://www.livescience.com/17455-butterfly-effect-weather-prediction.html - Compare my diagrams to this?, The Circles.

## Table of Contents

### Independent Axis

- Independence of Axis
- Proof of the" Time Vector " and " Hypothesis " Complex Math
- Complex algebra - Dot Product
- Graphical Theory
- Graphical Theory 2
- i - pairs
- Bernoulli Distribution - Defining 'p'
- The Determination of x²
- Showing x² = dy/dx
- Showing Calculated Value of Pi
- Pi at a = 5000
- Vector Equations
- Summation(x)
- Showing i-squared = - 1
- square box
- cylinder
- square roots of X
- Showing the Derivative of (x) Squared = a
- Imaginary Planes

### Fine Tuning Time Space

### Four Dimensional Space

### Graphs

### Multiplication

### The Definition of i

### Construction of the i distribution

### Transformations

### Geometry of i

- Full Geometry of i - Proof 2
- Coefficients of i - The Construction ....
- Imaginary Pi(i) - Construction i
- RV(i) Coordinate System - Evaluator
- Proof 3 - Complex(Pi) Trigonometry Geometry Solution
- i geometry dimensions; a = 1
- Complex Geometry ' i '
- Speed of Light Constant: Time
- vector addition
- 2 i
- Kepler's Ellipse : on the Complex Number Line
- x- geometry
- Inverse Trig functions
- i[squared] and i
- Imaginary Parabola

### Commentary

### Art

### Ln(x)

### Time Clock

### Probabilities

- i - probabilities (part two) - reference points
- Evenly divided Integers of ' a '
- Normal vs RVsigma - Proof 6 - varifacation(i)
- Center Line e(x)
- Rectangler Probabilities - Sums of Areas
- Normal Circular Probabilities
- Triangular Normal Probabilities
- Direct Link: Area/Variance = Constant
- Independent Distributions
- Independent Distributions 2

### Analysis of the Normal Curve

### Prime Numbers

### Null Set

### Complex Trigonometry

### The Four Subspaces