Maintenance script: Automated internal link correction

2016-02-24T23:22:41Z

Automated internal link correction

← Older revision		Revision as of 23:22, 24 February 2016
Line 34:		Line 34:

	* [[TI-BASIC:Real_Mode\|Real]]		* [[TI-BASIC:Real_Mode\|Real]]
	* [[TI-BASIC:~~A+bi~~\|A+bi]][[Category:TI-BASIC]]		* [[TI-BASIC:A_Bi\|A+bi]][[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:40:11Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=RETHETAI.GIF
|summary=Puts the calculator into re^θ''i'' mode.
|syntax=re^θ''i''
|location=Press:
# MODE to access the mode menu.
# Use the arrow keys and ENTER to select re^θ''i''
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

The re^θ''i'' command puts the calculator into polar complex number mode. This means that:
* Taking square roots of negative numbers, and similar operations, no longer returns an error.
* Complex results are displayed in the form re^(θ''i'') (hence the name of the command)

The mathematical underpinning of this complex number format is due to the fact that if (x,y) is a point in the plane using the normal coordinates, it can also be represented using coordinates (r,θ) where r is the distance from the origin and θ is the angle that the line segment to the point from the origin makes to the positive x-axis (see [[TI-BASIC:Polar_Mode|Polar]] and [[TI-BASIC:Polargc|PolarGC]] for more information on polar coordinates and graphing). What does this have to do with complex numbers? Simple: if x+y''i'' is a complex number in normal (rectangular) form, and re^(θ''i'') is the same number in polar form, then (x,y) and (r,θ) represent the same point in the plane.

Of course, that has a lot to do with how you define imaginary exponents, which isn't that obvious.

An equivalent form to polar form is the form r[cos(θ)+''i''sin(θ)].

Unfortunately, the calculator seems to have some confusion about the use of [[TI-BASIC:Degree_Mode|degree]] and [[TI-BASIC:Radian_Mode|radian]] angle measures for θ in this mode (the answer is: you can only use radians -- degrees make no sense with complex exponents). When calculating a value re^(θ''i'') by using the [[TI-BASIC:E_Exponent|e^(]] command and plugging in numbers, the calculator assumes θ is a radian angle, whether it's in Degree or Radian mode. However, when ''displaying'' a complex number as re^(θ''i''), the calculator will display θ in radian or degree measure, whichever is enabled. This may lead to such pathological output as:

Degree:re^θi
Done
e^(πi)
1e^(180i)
Ans=e^(180i)
0 (false)

It's recommended, then, to use [[TI-BASIC:Radian_Mode|Radian]] mode whenever you're in re^θ''i'' mode.

= Related Commands =

* [[TI-BASIC:Real_Mode|Real]]
* [[TI-BASIC:A+bi|A+bi]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Re Thetai - Revision history

Maintenance script: Automated internal link correction

Maintenance script: Initial automated import