Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

3.3 Übungen

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Robot: Automated text replacement (-Answer +Antwort))
K (Robot: Automated text replacement (-Solution +Lösung))
Zeile 24: Zeile 24:
|width="50%"| <math>\displaystyle\frac{(1+i\sqrt{3}\,)(1-i)^8}{(\sqrt{3}-i)^9}</math>
|width="50%"| <math>\displaystyle\frac{(1+i\sqrt{3}\,)(1-i)^8}{(\sqrt{3}-i)^9}</math>
|}
|}
-
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:1|Solution a|Solution 3.3:1a|Solution b|Solution 3.3:1b|Solution c|Solution 3.3:1c|Solution d|Solution 3.3:1d|Solution e|Solution 3.3:1e}}
+
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:1|Lösung a|Lösung 3.3:1a|Lösung b|Lösung 3.3:1b|Lösung c|Lösung 3.3:1c|Lösung d|Lösung 3.3:1d|Lösung e|Lösung 3.3:1e}}
===Übung 3.3:2===
===Übung 3.3:2===
Zeile 42: Zeile 42:
|width="33%"| <math>\displaystyle\Bigl(\frac{z+i}{z-i}\Bigr)^2 = -1</math>
|width="33%"| <math>\displaystyle\Bigl(\frac{z+i}{z-i}\Bigr)^2 = -1</math>
|}
|}
-
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:2|Solution a|Solution 3.3:2a|Solution b|Solution 3.3:2b|Solution c|Solution 3.3:2c|Solution d|Solution 3.3:2d|Solution e|Solution 3.3:2e}}
+
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:2|Lösung a|Lösung 3.3:2a|Lösung b|Lösung 3.3:2b|Lösung c|Lösung 3.3:2c|Lösung d|Lösung 3.3:2d|Lösung e|Lösung 3.3:2e}}
===Übung 3.3:3===
===Übung 3.3:3===
Zeile 58: Zeile 58:
|width="50%"| <math>iz^2+(2+3i)z-1</math>
|width="50%"| <math>iz^2+(2+3i)z-1</math>
|}
|}
-
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:3|Solution a|Solution 3.3:3a|Solution b|Solution 3.3:3b|Solution c|Solution 3.3:3c|Solution d|Solution 3.3:3d}}
+
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:3|Lösung a|Lösung 3.3:3a|Lösung b|Lösung 3.3:3b|Lösung c|Lösung 3.3:3c|Lösung d|Lösung 3.3:3d}}
===Übung 3.3:4===
===Übung 3.3:4===
Zeile 74: Zeile 74:
|width="50%"| <math>\displaystyle\frac{1}{z} + z = \frac{1}{2}</math>
|width="50%"| <math>\displaystyle\frac{1}{z} + z = \frac{1}{2}</math>
|}
|}
-
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:4|Solution a|Solution 3.3:4a|Solution b|Solution 3.3:4b|Solution c|Solution 3.3:4c|Solution d|Solution 3.3:4d}}
+
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:4|Lösung a|Lösung 3.3:4a|Lösung b|Lösung 3.3:4b|Lösung c|Lösung 3.3:4c|Lösung d|Lösung 3.3:4d}}
===Übung 3.3:5===
===Übung 3.3:5===
Zeile 90: Zeile 90:
|width="50%"| <math>(4+i)z^2+(1-21i)z=17</math>
|width="50%"| <math>(4+i)z^2+(1-21i)z=17</math>
|}
|}
-
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:5|Solution a|Solution 3.3:5a|Solution b|Solution 3.3:5b|Solution c|Solution 3.3:5c|Solution d|Solution 3.3:5d}}
+
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:5|Lösung a|Lösung 3.3:5a|Lösung b|Lösung 3.3:5b|Lösung c|Lösung 3.3:5c|Lösung d|Lösung 3.3:5d}}
===Übung 3.3:6===
===Übung 3.3:6===
<div class="ovning">
<div class="ovning">
Determine the solution to <math>\,z^2=1+i\,</math> both in polar form and in the form <math>\,a+ib\,</math>, where <math>\,a\,</math> and <math>\,b\,</math> are real numbers. Use the result to calculate <math>\; \tan \frac{\pi}{8}\,</math>.
Determine the solution to <math>\,z^2=1+i\,</math> both in polar form and in the form <math>\,a+ib\,</math>, where <math>\,a\,</math> and <math>\,b\,</math> are real numbers. Use the result to calculate <math>\; \tan \frac{\pi}{8}\,</math>.
-
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:6|Solution|Solution 3.3:6}}
+
</div>{{#NAVCONTENT:Antwort|Antwort 3.3:6|Lösung|Lösung 3.3:6}}

Version vom 13:34, 10. Mär. 2009

       Theorie          Übungen      

Übung 3.3:1

Write the following number in the form a+ib, where a and b are real numbers:

a) (i+1)12 b) 21+i312 
c) (43−4i)22  d) 1+i1+i312 
e) (3−i)9(1+i3)(1−i)8

Antwort | Lösung a | Lösung b | Lösung c | Lösung d | Lösung e

Übung 3.3:2

Solve the equations

a) z4=1 b) z3=−1 c) z5=−1−i
d) (z−1)4+4=0 e) z−iz+i2=−1 

Antwort | Lösung a | Lösung b | Lösung c | Lösung d | Lösung e

Übung 3.3:3

Complete the square of the following expressions

a) z2+2z+3 b) z2+3iz−41
c) −z2−2iz+4z+1 d) iz2+(2+3i)z−1

Antwort | Lösung a | Lösung b | Lösung c | Lösung d

Übung 3.3:4

Solve the equations

a) z2=i b) z2−4z+5=0
c) −z2+2z+3=0 d) z1+z=21

Antwort | Lösung a | Lösung b | Lösung c | Lösung d

Übung 3.3:5

Solve the equations

a) z2−2(1+i)z+2i−1=0 b) z2−(2−i)z+(3−i)=0
c) z2−(1+3i)z−4+3i=0 d) (4+i)z2+(1−21i)z=17

Antwort | Lösung a | Lösung b | Lösung c | Lösung d

Übung 3.3:6

Determine the solution to z2=1+i both in polar form and in the form a+ib, where a and b are real numbers. Use the result to calculate tan8.

Antwort | Lösung

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/3.3_%C3%9Cbungen“