$z$

$\frac{1}{z}$

Polardarstellung

z_1 = (2, 1)
u = Vector(z_1)
z_3: 1 / z_1
w = Vector(z_3)
ang_1 = If(Mod[Angle[z_1], 15°] ≟ 0, If[Angle[z_1] ≟ 180°, "", FractionText[Angle[z_1] / (180°)]], "" + (Angle[z_1] / (180°)))
ang_3 = If(Mod[Angle[z_3], 15°] ≟ 0, If[Angle[z_3] ≟ 180°, "", FractionText[Angle[z_3] / (180°)]], "" + (Angle[z_3] / (180°)))
abs_1: abs(z_1)
abs_3: abs(z_3)
im_1 = If(imaginary(z_1) ≠ 0, If[abs(imaginary(z_1)) ≠ 1, (abs(imaginary(z_1)) * "j"), "j"], "")
im_3 = If(imaginary(z_3) ≠ 0, If[abs(imaginary(z_3)) ≠ 1, (abs(imaginary(z_3)) * "j"), "j"], "")
re_1 = If(real(z_1) ≟ 0, "", ("" * real(z_1)))
re_3 = If(real(z_3) ≟ 0, "", ("" * real(z_3)))
plus_1 = If(imaginary(z_1) < 0, "-", If[imaginary(z_1) ≟ 0, "", If[real(z_1) ≟ 0, "", "+"]])
plus_3 = If(imaginary(z_3) < 0, "-", If[imaginary(z_3) ≟ 0, "", If[real(z_3) ≟ 0, "", "+"]])
zero_1 = If(real(z_1) ≟ 0 ∧ imaginary(z_1) ≟ 0, "0", "")
zero_3 = If(real(z_3) ≟ 0 ∧ imaginary(z_3) ≟ 0, "0", "")
L_1 = Sequence(Circle[(0, 0), i], i, 1, 10)
a = true
P: (10, 0)
N: (0, 0)
alpha1 = Angle(P, N, z_1)
alpha2 = Angle(z_1, N, P)
beta1 = Angle(P, N, z_3)
beta2 = Angle(z_3, N, P)
cart_3: "\frac{1}{z} = " + (LaTeX[zero_3]) + "" + (LaTeX[re_3]) + "" + (LaTeX[plus_3]) + "" + (LaTeX[im_3]) + ""
cart_{1}: "\textcolor{#0000ff}{ z = " + (LaTeX[zero_1]) + "" + (LaTeX[re_1]) + "" + (LaTeX[plus_1]) + "" + (LaTeX[im_1]) + " }"
polar_3: "\frac{1}{z} = " + (LaTeX[abs_3]) + " \;e^{" + (LaTeX[ang_3]) + "πj}"
polar_{1}: "\textcolor{#0000ff}{ z=" + (LaTeX[abs_1]) + " \;e^{ " + (LaTeX[ang_1]) + "πj} }"