R2 – Roots – Expressions
This post looks at the roots of expressions in R2. Calculate the full root of an R2 expression as the root of the Counter times the root of the Unitary. This applies whether the Counter is known or is a variable. Example 1 Example 2 Example 3 The multiplications below show that (x^ + xi^)2 = […]
R2 – Roots – Simple
This post provides some simple examples of R2 roots. The calculations behind some of the examples are also shown. Examples Firstly, here are some examples of the roots of i^. Secondly, here are examples of the roots of iv. Finally, here are some examples of non unitary roots. Sample Calculations These calculations show how these […]
R2 – Roots – Definition
This post on R2 roots covers the definition of roots and how roots are derived from the R2 multiplication table. Examples of square, cube and higher roots are given. Definition Wikipedia defines the square root as ‘a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or ) […]
R2 – Division – Advanced
This post covers more advanced math division in R2 including multiplicative inverses and the use of simultaneous equations. R2 Division Table / 1^ 1v i^ iv 1^ 1^ 1v iv i^ 1v 1v 1^ i^ iv i^ i^ iv 1^ 1v iv iv i^ 1v 1^ Inverses The theorems of multiplicative inverses describe the features […]
R2 – Division – Flipping
Flipping in R2 division can be applied to the individual Opposite Values or to the result to reverse their signs. R2 Division Table / 1^ 1v i^ iv 1^ 1^ 1v iv i^ 1v 1v 1^ i^ iv i^ i^ iv 1^ 1v iv iv i^ 1v 1^ Flipping Opposite Values in R2 Flipping Counters […]
R2 – Division – Definition
What is R2 Division? R2 division is the inverse of R2 multiplication. The result of division of an operand by an operator is described by a math expression. Multiplying the operator with the result gives the operand. For example: It is a scalar type operation that takes into account the Opposite Signs. As the inverse of […]
R2 – Multiplication – Dot Product
Dot product multiplication in R2 uses the same approach as in classical maths by using the formula: Dot product of a.b = (ax*bx) + (ay*by) where ax, bx, ay and by are the Counters of the Opposite Values a and b. For example: The dot product is based on the Counters of the Opposite Values […]
R2 – Multiplication -Trigonometry
This post covers features of a point in R2 and two methods for the multiplication of points. The first method is to multiply the R2 coordinates directly. The second method is to use multiplication formulae based on R2 trigonometry. Features of a Point The distance R of any point (a, b) from the origin is […]
R2 – Multiplication – Simple
This post looks at some simple multiplication of Opposite Values together and using counters. The examples show the commutativity, associativity and distributivity of R2 math multiplication. R2 Unitary Multiplication Table * 1^ 1v i^ iv 1^ 1^ 1v i^ iv 1v 1v 1^ iv i^ i^ i^ iv 1v 1^ iv iv i^ 1^ 1v […]
R2 – Multiplication – Definition
What is R2 Multiplication? Multiplication in R2 is similar to multiplication of complex numbers in classical maths. It is a scalar type operation that takes into account rotation through the Opposite Signs. It can be considered a ‘times-add’ operation with the Opposite Sign of the result dependent on the R2 multiplication table. This means […]