3.2 Übungen
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
K (Robot: Automated text replacement (-Exercises +Übungen)) |
K (Robot: Automated text replacement (-Exercise +Übung)) |
||
| Zeile 7: | Zeile 7: | ||
|} | |} | ||
| - | === | + | ===Übung 3.2:1=== |
<div class="ovning"> | <div class="ovning"> | ||
Given the complex numbers <math>\,z=2+i\,</math>, <math>\,w=2+3i\,</math> and <math>\,u=-1-2i\,</math>. Mark the following numbers on the complex plane: | Given the complex numbers <math>\,z=2+i\,</math>, <math>\,w=2+3i\,</math> and <math>\,u=-1-2i\,</math>. Mark the following numbers on the complex plane: | ||
| Zeile 23: | Zeile 23: | ||
</div>{{#NAVCONTENT:Answer|Answer 3.2:1|Solution a|Solution 3.2:1a|Solution b|Solution 3.2:1b|Solution c|Solution 3.2:1c|Solution d|Solution 3.2:1d}} | </div>{{#NAVCONTENT:Answer|Answer 3.2:1|Solution a|Solution 3.2:1a|Solution b|Solution 3.2:1b|Solution c|Solution 3.2:1c|Solution d|Solution 3.2:1d}} | ||
| - | === | + | ===Übung 3.2:2=== |
<div class="ovning"> | <div class="ovning"> | ||
Draw the following sets in the complex number plane | Draw the following sets in the complex number plane | ||
| Zeile 44: | Zeile 44: | ||
</div>{{#NAVCONTENT:Answer|Answer 3.2:2|Solution a|Solution 3.2:2a|Solution b|Solution 3.2:2b|Solution c|Solution 3.2:2c|Solution d|Solution 3.2:2d|Solution e|Solution 3.2:2e|Solution f|Solution 3.2:2f}} | </div>{{#NAVCONTENT:Answer|Answer 3.2:2|Solution a|Solution 3.2:2a|Solution b|Solution 3.2:2b|Solution c|Solution 3.2:2c|Solution d|Solution 3.2:2d|Solution e|Solution 3.2:2e|Solution f|Solution 3.2:2f}} | ||
| - | === | + | ===Übung 3.2:3=== |
<div class="ovning"> | <div class="ovning"> | ||
The complex numbers <math>\,1+i\,</math>, <math>\,3+2i\,</math> and <math>\,3i\,</math> constitute three corners of a square in the complex number plane. Determine the square's fourth corner. | The complex numbers <math>\,1+i\,</math>, <math>\,3+2i\,</math> and <math>\,3i\,</math> constitute three corners of a square in the complex number plane. Determine the square's fourth corner. | ||
</div>{{#NAVCONTENT:Answer|Answer 3.2:3|Solution|Solution 3.2:3}} | </div>{{#NAVCONTENT:Answer|Answer 3.2:3|Solution|Solution 3.2:3}} | ||
| - | === | + | ===Übung 3.2:4=== |
<div class="ovning"> | <div class="ovning"> | ||
Determine the magnitude of | Determine the magnitude of | ||
| Zeile 65: | Zeile 65: | ||
</div>{{#NAVCONTENT:Answer|Answer 3.2:4|Solution a|Solution 3.2:4a|Solution b|Solution 3.2:4b|Solution c|Solution 3.2:4c|Solution d|Solution 3.2:4d}} | </div>{{#NAVCONTENT:Answer|Answer 3.2:4|Solution a|Solution 3.2:4a|Solution b|Solution 3.2:4b|Solution c|Solution 3.2:4c|Solution d|Solution 3.2:4d}} | ||
| - | === | + | ===Übung 3.2:5=== |
<div class="ovning"> | <div class="ovning"> | ||
Determine the argument of | Determine the argument of | ||
| Zeile 81: | Zeile 81: | ||
</div>{{#NAVCONTENT:Answer|Answer 3.2:5|Solution a|Solution 3.2:5a|Solution b|Solution 3.2:5b|Solution c|Solution 3.2:5c|Solution d|Solution 3.2:5d}} | </div>{{#NAVCONTENT:Answer|Answer 3.2:5|Solution a|Solution 3.2:5a|Solution b|Solution 3.2:5b|Solution c|Solution 3.2:5c|Solution d|Solution 3.2:5d}} | ||
| - | === | + | ===Übung 3.2:6=== |
<div class="ovning"> | <div class="ovning"> | ||
Write the following numbers in polar form | Write the following numbers in polar form | ||
Version vom 13:24, 10. Mär. 2009
| Theory | Übungen |
Übung 3.2:1
Given the complex numbers \displaystyle \,z=2+i\,, \displaystyle \,w=2+3i\, and \displaystyle \,u=-1-2i\,. Mark the following numbers on the complex plane:
| a) | \displaystyle z\, and \displaystyle \,w | b) | \displaystyle z+u\, and \displaystyle \,z-u |
| c) | \displaystyle 2z+w | d) | \displaystyle z-\overline{w}+u |
Answer
Laden...
Solution a
Solution b
Solution c
Solution d
Übung 3.2:2
Draw the following sets in the complex number plane
| a) | \displaystyle 0\le \mbox{Im}\, z \le 3 | b) | \displaystyle 0 \le \mbox{Re} \, z \le \mbox{Im}\, z \le 3 |
| c) | \displaystyle |z|=2 | d) | \displaystyle |z-1-i|=3 |
| e) | \displaystyle \mbox{Re}\, z = i + \bar z | f) | \displaystyle 2<|z-i|\le3 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Übung 3.2:3
The complex numbers \displaystyle \,1+i\,, \displaystyle \,3+2i\, and \displaystyle \,3i\, constitute three corners of a square in the complex number plane. Determine the square's fourth corner.
Answer
Solution
Übung 3.2:4
Determine the magnitude of
| a) | \displaystyle 3+4i | b) | \displaystyle (2-i) + (5+3i) |
| c) | \displaystyle (3-4i)(3+2i) | d) | \displaystyle \displaystyle\frac{3-4i}{3+2i} |
Answer
Solution a
Solution b
Solution c
Solution d
Übung 3.2:5
Determine the argument of
| a) | \displaystyle -10 | b) | \displaystyle -2+2i |
| c) | \displaystyle (\sqrt{3} +i)(1-i) | d) | \displaystyle \displaystyle\frac{i}{1+i} |
Answer
Solution a
Solution b
Solution c
Solution d
Übung 3.2:6
Write the following numbers in polar form
| a) | \displaystyle 3 | b) | \displaystyle -11i |
| c) | \displaystyle -4-4i | d) | \displaystyle \sqrt{10} + \sqrt{30}\,i |
| e) | \displaystyle \displaystyle\frac{1+i\sqrt{3}}{1+i} | f) | \displaystyle \displaystyle\frac{(2+2i)(1+i\sqrt{3}\,)}{3i(\sqrt{12} -2i)} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
