Übungsaufgaben zur Vorlesung Analsis1

Aufgabe 1




Sei2 1 4: =
+
EC

sei w 3 i
=
+
C
=




2 w
+
1
=
+


4i
+


3 -
i 4 3i
= +




2.W (1
=
-

4i). (3 i) +
3 i
= + -
12; -
4i2 3
=
-
11i 4 7 + = -
11:


2W (1
=
+
4i)(3 i) +
3 i 12i
= + +
4i2
+

3 13;
=
+ -

4
=
-
1 13i
+
1
=
-
x 13i)
+
=
- (1413 770
=
=470 0i
+




E 4
=




=(3-i) 3i41:= =




w2 (3
= +
i)2 9 6i i2 8 61
= +
+ =
+

Re(w) 8
=> =




im () im)
=


imE).
=




=
I Il 11

-L 17
homplex
honj.
erweiterm




In

Aufgabe z 1




-




in
.


-




M {2
= 9:
= -
z= Rez 3, -1-(m2 23
=




M2 {2e
=
): 12 -
1 +


ic2) Betrag:Kreis
= mitRadius r:<crc2 und bei
Mittelpunkt 1:


M3 [2 =):12
= -
x 12
=




113
+
)
=
12 -
x 12 =
+
1)

1
M3 {2 k:Re(z)
=
=
=
=

83 1
(X x
=
-


4 (x c) 4
+ =
+
+




1 3x 0
= =




My {2= D:12 11
= +
-12 -

i) 12 =
-


13 1
=

Mu [ze):
=
Retz) - ((miz)) 5
=>
>
12 12 (2+ -
i) = 12 -
11

1 3(x (2
=
+

y2
+
x
=
2
(y x12=(x x2 y)
+ -
-

+




LC =


x yc
=
-
x


↓
x 0 -