Lösungen/Solutions/
B1S1Ue/Ex8

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A  =Anhang/  Annexe / Appendice

Remove["Global`@*"]

Ueb/Ex 1      W

z = 3 + 4 I

a

Conjugate[z]

b

Abs[z]

c

z^2

d

1/z

e

1/Abs[z]

f

z Conjugate[z]

g

Conjugate[z]/Abs[z^2]

h

Abs[Conjugate[z]]

Ueb/Ex 2      W

z1 = 1 - I; z2 = 1 + I;

a

z1 z2

b

z1/z2

c

Abs[z1/z2]

d

(z1 + z2)/z2

e

(2  z2 + z1)/(4  z2)

f

z1^2 z2^3

Ueb/Ex 3      W

Remove[z]

z1 = -1 - I

Solve[z^2 == z1, {z}]

Solve[z^3 == z1, {z}]

Solve[z^4 == z1, {z}]

Solve[z^5 == z1, {z}]

Ueb/Ex 4      W

Solve[x^2 + x + 1 == 0, {x}]

Ueb/Ex 5      W

z1 = 2 + I

Show[
        Graphics[
          Append[{PointSize[0.03]}, 
            Map[Point, 
              Table[{Re[z1^k], Im[z1^k]}, {k, 2, 
                  4}]]]
]];

ListPlot[Table[{Re[z1^k], Im[z1^k]}, {k, 2, 4}], 
        PlotStyle -> {PointSize[ .03]}];

z2 = 1/Sqrt[2] (1 + I)

n=10

ListPlot[Table[{Re[z2^k], Im[z2^k]}, {k, 0, 10}], 
        PlotStyle -> {PointSize[ .03]}];

n=40

ListPlot[Table[{Re[z2^k], Im[z2^k]}, {k, 0, 40}], 
        PlotStyle -> {PointSize[ .015]}];