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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