SkipCaptcha, Automoderated users, edit
3,266
edits
SamHB
Joined April 28, 2008
60 watt light bulbs.
:A huge rewrite, that I think puts complex numbers into the appropriate perspective in math, science, and technology. Previous writing on this subject seemed to present it in a way that I found somewhat dismissive. I have demoted some material, though I don't think I have removed anything outright. The reason is that the powers that be really don't like removal of stuff. I consider some of the material in this page to be irrelevant to a pedagogically proper presentation, and would like to take it out. I welcome discussion. Right here in the castle; it's OK. Or on the talk page. [[User:SamHB|SamHB]] 14:33, 28 November 2008 (EST)
:A huge rewrite, that I think puts complex numbers into the appropriate perspective in math, science, and technology. Previous writing on this subject seemed to present it in a way that I found somewhat dismissive. I have demoted some material, though I don't think I have removed anything outright. The reason is that the powers that be really don't like removal of stuff. I consider some of the material in this page to be irrelevant to a pedagogically proper presentation, and would like to take it out. I welcome discussion. Right here in the castle; it's OK. Or on the talk page. [[User:SamHB|SamHB]] 14:33, 28 November 2008 (EST)
===Complex analytic functions===
===Complex analytic functions===
[[User:SamHB|SamHB]] 14:33, 28 November 2008 (EST)
[[User:SamHB|SamHB]] 14:33, 28 November 2008 (EST)
==On Complex Numbers and Light Bulbs==
It has been suggested, at [[Conservapedia:Critical_Thinking_in_Math]], that the ratings of light bulbs can illustrate the irrelevance of complex numbers to real-world issues. This is in fact an uncannily bad choice of analogy, because light bulbs are commonly operated on alternating current, and the analysis and design of AC circuits in one of the areas in which complex numbers are used most successfully.
At an operating frequency of 60 Hz, light bulbs do not exhibit much phase shift, that is, much inductive or capacitive reactance, but the effects still exist. Let's go through some of the many ways in which electrical engineers measure things in terms of complex numbers.
*What is commonly called ''resistance'' at DC, that is, the ratio of voltage over current, becomes the complex quantity ''impedance'', because the voltage and current may not be in phase with each other.
*''Impedance'', the true ratio of voltage over current, is a complex number.
*The real part of the impedance is called the ''resistance''.
*The imaginary part of the impedance is called the ''reactance''.
*Depending on the sign of the reactance, it is characterized as ''capacitive reactance'' or ''inductive reactance''. ''Capacitors'' and ''inductors'' are electronic components designed to exhibit these reactances in fairly pure form.
*The reciprocal of the impedance, as a complex number, is the ''conductance''.
*The real part of the conductance is called the ''admittance''. Because of the properties of complex division, it is not the reciprocal of the resistance.
*The imaginary part of the conductance is called the ''susceptance''. It is not the reciprocal of the reactance.
*Because of phase differences, the power actually consumed by a device may not be the product of the voltage and current. For this reason, devices may be rated in ''volt-amperes'', or in ''watts''. Because of the low frequency involved, a 60 watt light bulb is also very nearly a 60 volt-ampere light bulb.
[[User:SamHB|SamHB]] 19:05, 25 December 2008 (EST)