$w$

$z_1$

$z_2$

Polardarstellung

z_1 = (0, 2)
w_{1}: sqrt(z_1)
w_{2}: (-w_{1})
u = Vector(z_1)
w = Vector(w_{1})
ang_1 = If(Mod[Angle[z_1], 15°] ≟ 0, If[Angle[z_1] ≟ 180°, "", FractionText[Angle[z_1] / (180°)]], "" + (Angle[z_1] / (180°)))
abs_1: abs(z_1)
abs_3: abs(w_{1})
im_1 = If(imaginary(z_1) ≟ 0, "", If[abs(imaginary(z_1)) ≟ 1, "j", abs(imaginary(z_1)) + "j"])
im_{w1} = If(imaginary(w_{1}) ≟ 0, "", If[abs(imaginary(w_{1})) ≟ 1, "j", abs(imaginary(w_{1})) + "j"])
re_1 = If(real(z_1) ≟ 0, "", "" + (real(z_1)))
re_{w1} = If(real(w_{1}) ≟ 0, "", "" + (real(w_{1})))
plus_1 = If(imaginary(z_1) ≟ 0, "", If[imaginary(z_1) < 0, "-", If[real(z_1) ≟ 0, "", "+"]])
plus_{w1} = If(imaginary(w_{1}) ≟ 0, "", If[imaginary(w_{1}) < 0, "-", If[real(w_{1}) ≟ 0, "", "+"]])
zero_{w1} = If(real(w_{1}) ≟ 0 ∧ imaginary(w_{1}) ≟ 0, "0", "")
zero_1 = If(real(z_1) ≟ 0 ∧ imaginary(z_1) ≟ 0, "0", "")
L_1 = Sequence(Circle[(0, 0), i], i, 1, 10)
a = false
P: (10, 0)
N: (0, 0)
alpha1 = Angle(P, N, z_1)
alpha2 = Angle(z_1, N, P)
b = Vector(w_{2})
zero_{w2} = If(real(w_{2}) ≟ 0 ∧ imaginary(w_{2}) ≟ 0, "0", "")
ang_{w2} = If(Mod[Angle[w_{2}], 15°] ≟ 0, If[Angle[w_{2}] ≟ 180°, "", FractionText[Angle[w_{2}] / (180°)]], "" + (Angle[w_{2}] / (180°)))
ang_{w1} = If(Mod[Angle[w_{1}], 15°] ≟ 0, If[Angle[w_{1}] ≟ 180°, "", FractionText[Angle[w_{1}] / (180°)]], "" + (Angle[w_{1}] / (180°)))
abs_{w}: abs(w_{1})
im_{w2} = If(imaginary(w_{2}) ≟ 0, "", If[abs(imaginary(w_{2})) ≟ 1, "j", abs(imaginary(w_{2})) + "j"])
plus_{w2} = If(imaginary(w_{2}) ≟ 0, "", If[imaginary(w_{2}) < 0, "-", If[real(w_{2}) ≟ 0, "", "+"]])
re_{w2} = If(real(w_{2}) ≟ 0, "", "" + (real(w_{2})))
cartesiantext: "\textcolor{#0000ff}{w = " + (LaTeX[zero_1]) + "" + (LaTeX[re_1]) + "" + (LaTeX[plus_1]) + "" + (LaTeX[im_1]) + " } \\ \\z_1 = " + (LaTeX[zero_{w1}]) + "" + (LaTeX[re_{w1}]) + "" + (LaTeX[plus_{w1}]) + "" + (LaTeX[im_{w1}]) + " \\ \\z_2 =" + (LaTeX[zero_{w2}]) + "" + (LaTeX[re_{w2}]) + "" + (LaTeX[plus_{w2}]) + "" + (LaTeX[im_{w2}]) + ""
polartext: "\textcolor{#0000ff}{ w = " + (LaTeX[abs_1]) + " \;e^{ " + (LaTeX[ang_1]) + "πj} } \\ \\
z_1 = " + (LaTeX[abs_{w}]) + " \;e^{" + (LaTeX[ang_{w1}]) + "πj} \\
z_2 = " + (LaTeX[abs_{w}]) + " \;e^{" + (LaTeX[ang_{w2}]) + "πj}"
beta1 = Angle(P, N, w_{1})
gamma1 = Angle(P, N, w_{2})
gamma2 = Angle(w_{2}, N, P)
beta2 = Angle(w_{1}, N, P)