複數的極式
Author: 藍邦偉  老師

$ O $

$ 複數的極式 $

$ A $

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, 7)
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.64 * Corner[1] + 0.36 * 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, 10)
A = Point(list4)
a = Segment(O, A)
B: (x(A), 0)
b = Segment(A, B)
θ = Angle((1, 0), O, A)
list2 = Sequence((15 * k)°, k, 0, 23)
list3 = Sequence(Ray[(0, 0), (cos(Element[list2, k]), sin(Element[list2, k]))], k, 1, 24)
r = Distance(O, A)
text1: "$ A=a+bi $
$=\sqrt{a²+b²}\left( \frac{a}{\sqrt{a²+b²}}+\frac{b}{\sqrt{a²+b²}}i  \right) $
$=\sqrt{" + (LaTeX[x(A)^(2) + y(A)^(2)]) + "}(cos" + (LaTeX[θ]) + "+isin" + (LaTeX[θ]) + ")$
$=" + (LaTeX[sqrt(x(A)^(2) + y(A)^(2))]) + "(cos" + (LaTeX[θ]) + "+isin" + (LaTeX[θ]) + ")$
$=" + (LaTeX[r]) + "(" + (LaTeX[SurdText[cos(θ)]]) + "" + (LaTeX[If[sin(θ) < 0, "-", "+"]]) + "" + (LaTeX[SurdText[abs(sin(θ))]]) + "i)$"