R2 – Exponentiation – Fractions, Flip Sign and Rules
This post covers the rules of R2 exponentiation. It also describes the use of fractions and the flip sign with exponentiation along with some examples. Fractions Exponents in fractions represent multiplication roots. As described in an earlier post, the root of an expression can be expressed as the root of the counter multiplied by the […]
R2 – Exponentiation – Definition
Introduction This post covers the definition of R2 Exponentiation in Wave Numbers. It also includes reciprocals and examples. In Wikipedia, exponentiation is defined as follows: ‘Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as “b raised to the power of n”. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that […]
R2 – Roots – Advanced
This post covers the use or De Moivre’s formula as an advanced method of calculating roots in R2. Some examples are provided. Formula The roots of any Opposite Value can be calculated using the formula below which is based on De Moivre’s formula. This formula relies on the fact that the root of an Opposite […]
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 […]