3. How do calculators deal with imaginary numbers?

How do calculators deal with imaginary numbers?

Strangely enough I was just working on a calculator for a small project. The answer lies in grammars, (not the English kind of "grammar", commas, full stops, and so on... the computer science kind, rules that govern how language is generated.)

So here is an example of a basic calculator grammar (ignore any strange naming conventions, this wasn't for public consumption):

<bracketCalculation>    ::= (<calculation>)|<calculation>
<calculation>           ::= <bracketCalculation><operator><bracketCalculation>|<number>
<operation>             ::= +|-|x|\

//real, natural and rational numbers. <number> ::= 0<D>|-<B>|<posDigit><C> <D> ::= .<E>|ϵ <B> ::= <posDigit><C>|0.<E> <C> ::= <digit>C|.<E>|ϵ <E> ::= <digit>F <F> ::= <digit>F|ϵ <posDigit> ::= 1|2|3|4|5|6|7|8|9 <digit> ::= 0|<posDigit>

The program runs though the calculation string, splits it up into tokens and then translates it into it's corresponding internal representation, based on the patterns it matches.

So for imaginary numbers it would do a similar thing, but a lot simpler, this grammar only has to match i with -1, so:

i  ::= -1
/r/askscience Thread
Previous
Next

Recently removed from /r/askscience

What does alcohol do to your blood sugar? I thought it spiked it? Is the Flynn effect still going? Does being sick impair the body’s ability to form memories during that time? Does having autoimmune disorder (atopic disease in my mind, but also otherwise) lead to an increased risk of immune cell cancer? What determines whether we can create a vaccine for an illness or not? Why is gluten intolerance a new phenomenon / on the rise? What's the difference in your brain between seeing an object, thinking about that object, and visualizing an object? Why are we no longer contagious even if not all influenza symptoms are gone? AskScience AMA Series: We're Experts on Influenza (aka the Flu). AUA! I’ve been browsing YouTube a lot and lately I’ve fallen into a loop of videos where uploaders ‘rescue’ sea turtles by cleaning their shells of debris and barnacles. These turtles look suspiciously like pond sliders, is that even possible? Could breathing through the mouth alter a 13 year olds face and if so how long would it take? When nucleons bind to form a nucleus, does each nucleon "retain ownership" over its quarks (is each nucleon a truly unique entity)? Or is it possible for quarks to swap from one nucleon to another? Or does it not make sense to talk so exactly about them? Do other terrestrial planets have metals like gold, silver, etc? Why does coding work? As microchips get smaller and smaller, won't single event upsets (SEU) caused by cosmic radiation get more likely? Are manufacturers putting any thought to hardening the chips against them?

More Random Comments

This is ridiculous Memorial dedicated to Savita Halappanavar, an Indian woman living in Ireland, who died of sepsis after being denied an abortion on the grounds that the fetus she was miscarrying still had a detectable heartbeat. Born color blind, decided to make color picking a little simple for my game. [serious]What's the saddest thing that ever happened to you? Dr. Feldman's 1st [Co-Authored] Article On MBI [Serious] When was the first time you had experienced racism? Mindfulness, which revolves around focusing on the present and accepting negative thoughts without judgment, is associated with reduced levels of procrastination. This suggests that developing mindfulness could help procrastinators cope with their procrastination. Game of Thrones fans who want a redo Those of you who have been in mental hospitals,workers OR patients, What was the most traumatic experience for you while in there? Feel Free to Correct me or Add anything The spinoff movie we all want to see Why do we have an Electoral College decide the fate of our country instead of the people who numerically pay the larger price for what happens? SJW's Who Are Actually Fans New Banable Offences on Owen's Livechat [please read] Help a guy get over a breakup?