imaginäre Zahlenachse

i

-i

Re(z)

Im(z)

n

z

e_x = (1, 0)
P = Point(xAxis)
a_y: (0.4, 0.4) * x(P)
a_x: (x(P), 0.0)
e_y = (0.4, 0.4)
e_z = (0, 1)
c: x^(2.0) + y^(2.0) = x(P)^(2.0)
A = Point(c)
d = Ellipse(Point[e_x], Point[e_y], Point[e_x * sqrt(2.0) / 2.0 + e_y * sqrt(2.0) / 2.0])
e = Conic(Point[e_x], Point[e_y], Point[-(e_x)], Point[-(e_y)], Point[(e_x + e_y) * sqrt(2.0) / 2.0])
S: (0.0, 0.0) + a_y
U: (0.0, 0.0) - a_x
V: (0.0, 0.0) + sqrt(2.0) / 2.0 * (a_x + a_y)
R: (0.0, 0.0) + a_x
T: (0.0, 0.0) - a_y
f = Conic(R, S, T, U, V)
C = Point(f)
Text1: (x(C) - y(C)) / 0.4 + " + " + (y(C) / 0.4) + " ii"
z: x(C) - y(C) + " + " + (y(C) / 0.4) + " i"
u = Vector((0.0, 0.0), (0.0, 0.0) + 2.0 * e_y)
v = Vector((0.0, 0.0), (0.0, 0.0) - 2.0 * e_y)
Liste1 = Sequence((0.0, 0.0) + t * 0.2 * e_y, t, -7.0, 7.0)
a = Line(C, xAxis)
b = Line(C, u)
D = Intersect(b, xAxis)
g = Line((0.0, 0.0) - 2.0 * e_y, (0.0, 0.0) + 2.0 * e_y)
E = Intersect(a, g)
h = Segment(C, D)
i = Segment(C, E)
A2 = 1
C2: y(C) / 0.4
B2: x(C) - y(C)
A3: A2 + 1.0
B3: $B$2 * B2 - $C$2 * C2
C3: $C$2 * B2 + $B$2 * C2
A4: A3 + 1.0
B4: $B$2 * B3 - $C$2 * C3
C4: $C$2 * B3 + $B$2 * C3
A5: A4 + 1.0
B5: $B$2 * B4 - $C$2 * C4
C5: $C$2 * B4 + $B$2 * C4
A6: A5 + 1.0
B6: $B$2 * B5 - $C$2 * C5
C6: $C$2 * B5 + $B$2 * C5
A7: A6 + 1.0
B7: $B$2 * B6 - $C$2 * C6
C7: $C$2 * B6 + $B$2 * C6
A8: A7 + 1.0
B8: $B$2 * B7 - $C$2 * C7
C8: $C$2 * B7 + $B$2 * C7
A9: A8 + 1.0
B9: $B$2 * B8 - $C$2 * C8
C9: $C$2 * B8 + $B$2 * C8
A10: A9 + 1.0
B10: $B$2 * B9 - $C$2 * C9
C10: $C$2 * B9 + $B$2 * C9
A11: A10 + 1.0
B11: $B$2 * B10 - $C$2 * C10
C11: $C$2 * B10 + $B$2 * C10
A12: A11 + 1.0
B12: $B$2 * B11 - $C$2 * C11
C12: $C$2 * B11 + $B$2 * C11
A13: A12 + 1.0
B13: $B$2 * B12 - $C$2 * C12
C13: $C$2 * B12 + $B$2 * C12
A14: A13 + 1.0
B14: $B$2 * B13 - $C$2 * C13
C14: $C$2 * B13 + $B$2 * C13
A15: A14 + 1.0
B15: $B$2 * B14 - $C$2 * C14
C15: $C$2 * B14 + $B$2 * C14
A16: A15 + 1.0
B16: $B$2 * B15 - $C$2 * C15
C16: $C$2 * B15 + $B$2 * C15
A17: A16 + 1.0
B17: $B$2 * B16 - $C$2 * C16
C17: $C$2 * B16 + $B$2 * C16
A18: A17 + 1.0
B18: $B$2 * B17 - $C$2 * C17
C18: $C$2 * B17 + $B$2 * C17
A19: A18 + 1.0
B19: $B$2 * B18 - $C$2 * C18
C19: $C$2 * B18 + $B$2 * C18
A20: A19 + 1.0
B20: $B$2 * B19 - $C$2 * C19
C20: $C$2 * B19 + $B$2 * C19
A21: A20 + 1.0
B21: $B$2 * B20 - $C$2 * C20
C21: $C$2 * B20 + $B$2 * C20
A22: A21 + 1.0
B22: $B$2 * B21 - $C$2 * C21
C22: $C$2 * B21 + $B$2 * C21
P_1: (B2, C2)
P_2: (B3, C3)
P_3: (B4, C4)
P_4: (B5, C5)
P_5: (B6, C6)
P_6: (B7, C7)
P_7: (B8, C8)
P_8: (B9, C9)
P_9: (B10, C10)
P_{10}: (B11, C11)
P_{11}: (B12, C12)
P_{12}: (B13, C13)
P_{13}: (B14, C14)
P_{14}: (B15, C15)
P_{15}: (B16, C16)
P_{16}: (B17, C17)
P_{17}: (B18, C18)
P_{18}: (B19, C19)
P_{19}: (B20, C20)
P_{20}: (B21, C21)
P_{21}: (B22, C22)
Liste2: {P_1, P_2, P_3, P_4, P_5, P_6, P_7, P_8, P_9, P_{10}, P_{11}, P_{12}, P_{13}, P_{14}, P_{15}, P_{16}, P_{17}, P_{18}, P_{19}, P_{20}, P_{21}}
Liste3 = Sequence(x(Element[Liste2, i]) * e_x + y(Element[Liste2, i]) * e_y + e_z * (i - 1.0) / 25.0, i, 1.0, 21.0)
Liste4 = Sequence(Segment[Element[Liste3, i], Element[Liste3, i + 1.0]], i, 1.0, 20.0)
j: x(P)
B: x(A) * a_x + y(A) * a_y