Saturday, December 11, 2021

Casio fx-CP400: Complex Numbered Graphs Using 3D Parametric Graphing

Casio fx-CP400: Complex Numbered Graphs Using 3D Parametric Graphing


Note:  The procedure listed on today's post also applies to the Casio fx-CG 50 and fx-CG 500.  Since this involves the 3D Parametric Graphing mode, I don't think it will work on the ClassPad 300 or 330.

Here is a way to display complex-number functions: the use of 3D parametric graphing.   The general form will be:

x(s, t) = real(f(w)),   the real part of f(w)

y(s, t) = imag(f(w)),  the imaginary part of f(w)

z(s, t) = 0

where w = s + t*i,  i = √-1

Other computer programs, like Mathematica, uses t and r for variables for 3D parametric graphing.   Check the manual for details.

For the Classpad,  re is the real part function, and im in the imaginary part function.   In the following examples, f(w) can be algebraically simplified to separate the real and imaginary parts.   

I set the x grid and y grid to 50, which is the maximum amount of points allowed.  This allows for most detailed graphs possible.  I set the window to viewing the z axis from the top.  On the Classpad, this is done by either pressing the [ z ] button or setting the angle settings on the View Window to:

angle Θ: -09

angle Φ: 0

Please keep in mind, the graph displayed will be the results, or the range, of f(w);

(s + t*i) ->  (x + y*i) = f(s + t*i)

To see s and t, execute Trace mode.  Read x and y for the real and imaginary part of the result.

I am using the Classpad, fx-CP400, because of the large screen which allows us to show the equations and the graph on one screen comfortably.  On each graph, I put f(w) as a text string on the graph screen.  For format, I set the line color to blue, green, or red (or any of the available colors) and I set the area to Clear (eraser icon).  


w = s + t*i,   x = real(f(w)), y = imag(f(w)), z = 0, Radians mode selected

Example 1:

f(w) = (w - i)^2 

x = s^2 - (t - 1)^2

y = 2 * s * (t - 1)

z = 0

Example 2:

f(w) = e^w

x = e^s * cos t

y = e^s * sin t

z = 0

Example 3:  

f(w) = 1/w

x = s / (s^2 + t^2)

y = -t / (s^2 + t^2)

z = 0

Example 4:

f(w) = sin w

x = sin s * cosh t

y = cos s * sinh t

z = 0

Really cool to see.  


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