Lösungen/Solutions/
B1S2Ue/Ex10

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

vecLen[a_] := Sqrt[a . a];
look[a_] := {a, " or ",  N[a]}

Ueb/Ex 1      W

z1 = 4 + 2  I;  z2 = 3 - I; {z1,  z2}

a

z1 - z2

b

z1  +  z2

c

z1  z2

d

z1/z2

Ueb/Ex 2      W

z = 1 + I

1/z

Conjugate[z]/Abs[z]^2 == 1/z

Re[1/z] +  I * Im[1/z] // Evaluate

z + 1/z

Ueb/Ex 3      W

a

P[1] = 3 + I; 
P[2] = 11 + I; 
P[3] = 14 + I;
P[4] = 14 + 3.5  I;
P[5] = 11 + 3.5  I;
P[6] = 5 + 3.5  I;
P[7] = 3 + 6  I;
P[8] = 11 + 6  I;
t1 = Table[P[n], {n, 1, 8}]

t2 = 2 t1

t3 = t2 + 5 + 7  I

φ  = 50 2 Pi/360

rot = Cos[φ] + I Sin[φ]

t4 =  rot t3

t4 =  rot t3 // N

ret1 = Re[t1]

ret4 = Re[t4]

imt1 = Im[t1]

imt4 = Im[t4]

p1 = Table[{Re[t1][[n]],  Im[t1][[n]]}, {n, 1, 8}]; 
    p4 = Table[{Re[t4][[n]],  Im[t4][[n]]}, {n, 1, 8}]; 
    p = Append[Join[p1, p4], {0, 0}]

pts = Table[Point[p[[n]]], {n, 1, 17}]

pts1 = Prepend[pts, PointSize[0.03]]

s1 = 
      Line[{p1[[1]], p1[[3]], p1[[4]], p1[[6]], p1[[7]], 
          p1[[8]], p1[[2]], p1[[1]], p1[[6]], p1[[7]], 
          p1[[1]]}]

s4 = 
      Line[{p4[[1]], p4[[3]], p4[[4]], p4[[6]], p4[[7]], 
          p4[[8]], p4[[2]], p4[[1]], p4[[6]], p4[[7]], 
          p4[[1]]}]

q = 
      Join[pts1, {s1, s4, Line[{{-3, 0}, {3, 0}}], 
          Line[{{0, 0}, {0, 3}}]}]

Show[Graphics[q], AspectRatio -> 1  $];