“Inconceivable!” – Vizzini
“You keep using that word. I do not think it means what you think it means.”
– Inigo Montoya, The Princess Bride

Definitions enable us to have a common understanding of a word or subject; they allow all to be in agreement when discussing or reading about a topic. Here are some words that may not be found in a standard mathematics dictionary.

## A

affix
Let z = a + ib in its geometric representation. Affix is the point in the complex plane corresponding to this number, i.e., the point with Cartesian coordinates (a,b), or by a vector with the origin (0,0). The affix is sometimes identified with the complex number itself.
Argand (or Gauss) plane
The complex plane is sometimes called the Argand plane because it is used in Argand diagrams. These are named after Jean-Robert Argand (1768–1822), who was an amateur mathematician and a keeper of a bookstore in Paris, although they were first described by Danish land surveyor and mathematician Caspar Wessel (1745–1818). The complex plane is basically a modified Cartesian plane where the x-axis and the y-axis have been dubbed the “real axis” and the “imaginary axis,” respectively.

## S

semi-straight line (ray)
A semi-straight line is a line which has a boundary or a defined point on one side and is infinite on the other side. The below semi-straight line is expressed as follows [X Y).

surds
The Latin meaning of the word “Surd” is deaf or mute. In earlier days, Arabian mathematicians called rational numbers and irrational numbers as audible and inaudible. Since surds form are made of irrational numbers, they were referred to as asamm (deaf, dumb) in Arabic language, and were later translated in Latin as surds.

Surds are expressions that contain a square root, cube root or other roots. They are roots of numbers that produce an irrational number as a result, with infinite decimals. Therefore, they are left in their root form to represent them more exactly. For example, √2, √3, √5, √6, √7.

## References

Clapham, Christopher, and James Nicholson. 2023. “The Concise Oxford Dictionary Of Mathematics”. Oxford University Press. https://www.oxfordreference.com/display/10.1093/acref/9780199235940.001.0001/acref-9780199235940;jsessionid=44F8961D71ECBCF233D1594FABBF6518.

“Illustrated Mathematics Dictionary”. 2023. mathsisfun.com. https://www.mathsisfun.com/definitions/.

“Mathwords”. 2023. mathwords.com. https://www.mathwords.com/.

### Affix

“Affix — from Wolfram MathWorld”. 2023. mathworld.wolfram.com. https://mathworld.wolfram.com/Affix.html.

“Affix of a complex number”. 2023. Encyclopedia of Mathematics. https://encyclopediaofmath.org/wiki/Affix_of_a_complex_number.

### Argand (or Gauss) plane

“Argand Diagram — From Wolfram Mathworld”. 2023. mathworld.wolfram.com. https://mathworld.wolfram.com/ArgandDiagram.html.

“Lesson Explainer: Argand Diagram”. 2023. nagwa. https://www.nagwa.com/en/explainers/280109891548/.

“Polar Representation of Complex Number on a Argand Plane”. 2023. BYJUS. https://byjus.com/maths/argand-plane-and-polar-representation-of-complex-number/.

### Surds

“Surds – Mathematics GCSE Revision”. 2023. revisionmaths.com. https://revisionmaths.com/gcse-maths-revision/number/surds.

“Surds (Maths): Definition, Examples & Rules | StudySmarter”. 2023. StudySmarter US. https://www.studysmarter.us/explanations/math/pure-maths/surds/.

⭐ “Surds – Definition, Types, Rules, And Problems”. 2023. BYJUS. https://byjus.com/maths/surds/.

⭐ “Surds And Indices – Definition, Types, Rules, And Practice Problems”. 2023. CUEMATH. https://www.cuemath.com/numbers/surds/.

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.

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