Saturday, December 18, 2021

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

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


Introduction


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


The view window was set 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.


For more details, please see last week's (12/11/2021) post.  


Examples


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


Example 1:


f(w) = 2^w


x = 2^s * cos(t * ln 2)

y = 2^s * sin(t * ln 2)

z = 0





Example 2:


f(w) = w^(1/2) = e^(1/2 * ln w)


x = re((s + t*i)^0.5)

y = im((s + t*i)^0.5)

z = 0





Example 3:  


f(w) = w^3 + 1


x = s^3 - 3*s*t^2 + 1

y = -t^3 + 3*s^2*t

z = 0





Example 4:


f(w) = 2 * cos(w/2)


x = 2 * cos(s/2) * cosh(t/2)

y = -2 * sin(s/2) * sinh(t/2)

z = 0





Eddie 


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