# [IAEP] Complex arithmetic (was Re: Looking for Concrete "Fraction Experiences")

mokurai at earthtreasury.org mokurai at earthtreasury.org
Thu Jul 14 13:06:06 EDT 2011

```On Thu, July 14, 2011 9:46 am, David Corking wrote:

> (Aspiring electrical technicians will probably also want to extend the
> concept to complex numbers.)

Addition and subtraction of complex numbers are easier in rectangular
coordinates than polar coordinates. Multiplication and division are the
opposite.

a + bi + c +di = (a + c) + (b + d)i

1/(r,theta) = (1/r, -theta)

But it can be done, of course.

1/(a + bi) = (a - bi)/(a^2 + b^2)

(a + bi)/(c + di)

= (a + bi)(c - di)/(c^2 + d^2)

= ((ac + bd) +(bc - ad)i/(c^2 + d^2)

I should do these up in Turtle Art, both as illustrations of coordinate
systems and as arithmetic, and add them to my Tutorials.

http://wiki.sugarlabs.org/go/Activities/TurtleArt/Tutorials#Mokurai.27s_Tutorials

> Thanks for your patience. David

--
Edward Mokurai
(默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر
ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://wiki.sugarlabs.org/go/Replacing_Textbooks

```