Editing Complex items

{{FoCW Header|the Complex value of items|From N over Q to C}}

Complex items can only enter the game by chance. They can not be bought for gold coins or real life money. Because of the rareness and the unability to compare them to other items, their price composition can only be understood with difficulty. The value is very independant and fluctuating at certain events or messages made public by the game designer.


= Introduction to '''C''' =

{| style="width:100%;" cellspacing="0" cellpadding="10"
|- style="vertical-align:center;"
| style="width:50%;" |
In the beginning the value of an item was defined by collective agreement to a positive integer number which we shall call a natural number '''(N)'''.
| style="width:30%;" |
 {0,1,2,3,4,..}
|}
{| style="width:100%;" cellspacing="0" cellpadding="10"
|- style="vertical-align:center;"
| style="width:50%;" |
But soon there was a need for a exact price due to the competition of the robot market. So even little fractions of money could mean a bit profit when huge quantities of items were traded. This is the beginning of the rational numbers '''(Q)'''.

| style="width:30%;" |
 {1/2, 2/3, 3/4, 1, 1.25, ..}
|}
At some point in EL-History rare [[stones]] were introduced. These could be found by change during [[harvestables|harvesting]] minerals or plants. Only a small number of players were able to pay the price which was demanded on the market. It became clear that the value could not depend on the value of another items as it occurs in [[item chains]].

At the 30th day in the month of Elandra, the year 0036, Age of the Eternals the idea was born that items can have imaginary values. This is even more true for rare items. A price for an item is established by supply and demand on the market channel. It is possible to differ between the real and the imaginary value. Consequently the value can be written as a complex number '''(C)'''.

The complex price '''Z''' consists of a fix real part '''A''' and a changing imaginary part '''B'''. It can be plotted in a complex plane. The player can only pay the absolute value. '''|Z|''' is always positive since it is build mathematicly of the square root of the sum of the quares of both parts '''A''' and '''B'''. The same law is applied in the Pythagorean equation.

= Calculation =

''Complex numbers are especially meaningful for very high amounts of money.''



== What is the value of a [[File:No More Tears Cape.png|25px]] [[No More Tears Cape]] ? ==

{| style="width:100%;" cellspacing="0" cellpadding="10"
|- style="vertical-align:center;"
| style="width:30%;" |
* A represents the minimum price
* B represents the interest
| style="width:20%;" |
* '''A''' = 400k
* '''B''' = 500k
* '''Z''' = 640k
| style="width:60%;" |
 with '''|Z|''' = SQR [('''A''')² + ('''B''')²]
| style="width:40%;" |
|}


== What is the value of a [[File:Animal Removal Stone.png|25px]] [[Removal Stones#Nexus Removal Stones|Nexus removal stone]] ? ==

{| style="width:100%;" cellspacing="0" cellpadding="10"
|- style="vertical-align:center;"
| style="width:30%;" |
* A represents the minimum price
* B represents the interest
| style="width:20%;" |
* '''A''' = 400k
* '''B''' = 870k
* '''Z''' = 957k
| style="width:60%;" |
 with '''|Z|''' = SQR [('''A''')² + ('''B''')²]
| style="width:40%;" |
|}


----
* Z will always be positive, even if '''B''' is a negative value. So in that sense we have never left our beloved natural numbers.

= Sale =

* The advantage of complex numbers over integer numbers is, that players can trade items not under regular price (price dumping).
* A post on market channel could look like this:
{| style="width:100%;" cellspacing="0" cellpadding="10"
|- style="vertical-align:center;"
| style="width:40%;" |
 [SolarStar @ 3]: Selling a NMT-cape for 400k + i*500k
| style="width:60%;" |

Last but not least, the price can also be formated from Cartesian into Polar form !!
| style="width:40%;" |
 [PolarStar @ 3]: Selling a NMT-cape for 640k e^i*51.3°
| style="width:60%;" |
|}
''Positive values of '''phi''' indicate how much more the player is willing to give in addition to the regular price.''