複數極式乘法與除法示例
Author: 藍邦偉  老師

$ O $

$ 複數極式的乘法與除法 $

$A$

1

$ 除法 $

$ 乘法 $

2

$ A $

$ B $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
list4 = Sequence(Sequence[(r * cos(15° * k), r * sin(15° * k)), k, 0, 23], r, 1, 13)
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.65 * Corner[1] + 0.35 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
list1 = Sequence(x^(2) + y^(2) = r^(2), r, 1, 15)
A = Point(list4)
B = Point(list4)
α = Angle((1, 0), O, A)
β = Angle((1, 0), O, B)
z_1: sqrt(x(A)^(2) + y(A)^(2))
z_2: sqrt(x(B)^(2) + y(B)^(2))
text3: "$ =" + (LaTeX[z_1 * z_2]) + " (cos" + (LaTeX[α + β]) + "+isin" + (LaTeX[α + β]) + ")$"
text2: "$=[\;" + (LaTeX[z_1]) + "(cos" + (LaTeX[α]) + "+isin" + (LaTeX[α]) + ") \;]$
         $\cdot [\;" + (LaTeX[z_2]) + "(cos" + (LaTeX[β]) + "+isin" + (LaTeX[β]) + ")\;]$"
text4: "$ Arg(z_1z_2)=Arg(z_1)+Arg(z_2) $
                     $=" + (LaTeX[α]) + "+" + (LaTeX[β]) + "$
                     $=" + (LaTeX[α + β]) + "$"
a = Segment(O, A)
b = Segment(O, B)
T1: "$ \frac{z_1}{z_2}=\frac{" + (LaTeX[x(A)]) + " " + (LaTeX[If[x(A) < 0, "-", "+"]]) + "" + (LaTeX[abs(x(A))]) + "\;i}{" + (LaTeX[x(B)]) + "" + (LaTeX[If[y(B) < 0, "-", "+"]]) + "" + (LaTeX[abs(y(B))]) + "\;i}$"
T2: "$ =\frac{|" + (LaTeX[z_1]) + "|(cos" + (LaTeX[α]) + "+isin" + (LaTeX[α]) + ")}{|" + (LaTeX[z_2]) + "|(cos" + (LaTeX[β]) + "+isin" + (LaTeX[β]) + ")} $"
T3: "$ =" + (LaTeX[FractionText[z_1 / z_2]]) + "  \left [ cos(" + (LaTeX[α]) + "-" + (LaTeX[β]) + ")$
      $+isin(" + (LaTeX[α]) + "-" + (LaTeX[β]) + ") ]  $"
T4: "$ =" + (LaTeX[FractionText[z_1 / z_2]]) + " (cos" + (LaTeX[α - β]) + "+isin" + (LaTeX[α - β]) + ")$"
text1: "$ z_1z_2$
$=(" + (LaTeX[x(A)]) + "" + (LaTeX[If[y(A) < 0, "-", "+"]]) + "" + (LaTeX[abs(y(A))]) + "\;i)(" + (LaTeX[x(B)]) + "" + (LaTeX[If[y(B) < 0, "-", "+"]]) + "" + (LaTeX[abs(y(B))]) + "\;i)$"
c = true
d = false
n = 0 (slider from 0 to 5, step 1)
T5: "$ Arg(\frac{z_1}{z_2})=Arg(z_1)-Arg(z_2) $
$=" + (LaTeX[α]) + "-" + (LaTeX[β]) + "$
$=" + (LaTeX[α - β]) + "$"
list2 = Sequence((15 * k)°, k, 0, 23)
list3 = Sequence(Ray[(0, 0), (cos(Element[list2, k]), sin(Element[list2, k]))], k, 1, 24)