3.2 Übungen
Aus Online Mathematik Brückenkurs 2
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| - | {{Ej vald flik|[[3.2 Polär form| | + | {{Ej vald flik|[[3.2 Polär form|Theory]]}} |
| - | {{Vald flik|[[3.2 Övningar| | + | {{Vald flik|[[3.2 Övningar|Exercises]]}} |
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| - | === | + | ===Exercise 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: | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 3.2:1|Lösning a|Lösning 3.2:1a|Lösning b|Lösning 3.2:1b|Lösning c|Lösning 3.2:1c|Lösning d|Lösning 3.2:1d}} | </div>{{#NAVCONTENT:Svar|Svar 3.2:1|Lösning a|Lösning 3.2:1a|Lösning b|Lösning 3.2:1b|Lösning c|Lösning 3.2:1c|Lösning d|Lösning 3.2:1d}} | ||
| - | === | + | ===Exercise 3.2:2=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Draw the following sets in the complex number plane | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 3.2:2|Lösning a|Lösning 3.2:2a|Lösning b|Lösning 3.2:2b|Lösning c|Lösning 3.2:2c|Lösning d|Lösning 3.2:2d|Lösning e|Lösning 3.2:2e|Lösning f|Lösning 3.2:2f}} | </div>{{#NAVCONTENT:Svar|Svar 3.2:2|Lösning a|Lösning 3.2:2a|Lösning b|Lösning 3.2:2b|Lösning c|Lösning 3.2:2c|Lösning d|Lösning 3.2:2d|Lösning e|Lösning 3.2:2e|Lösning f|Lösning 3.2:2f}} | ||
| - | === | + | ===Exercise 3.2:3=== |
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| - | + | 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:Svar|Svar 3.2:3|Lösning |Lösning 3.2:3}} | </div>{{#NAVCONTENT:Svar|Svar 3.2:3|Lösning |Lösning 3.2:3}} | ||
| - | === | + | ===Exercise 3.2:4=== |
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| - | + | Determine the magnitude of | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 3.2:4|Lösning a|Lösning 3.2:4a|Lösning b|Lösning 3.2:4b|Lösning c|Lösning 3.2:4c|Lösning d|Lösning 3.2:4d}} | </div>{{#NAVCONTENT:Svar|Svar 3.2:4|Lösning a|Lösning 3.2:4a|Lösning b|Lösning 3.2:4b|Lösning c|Lösning 3.2:4c|Lösning d|Lösning 3.2:4d}} | ||
| - | === | + | ===Exercise 3.2:5=== |
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| - | + | Determine the argument of | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 3.2:5|Lösning a|Lösning 3.2:5a|Lösning b|Lösning 3.2:5b|Lösning c|Lösning 3.2:5c|Lösning d|Lösning 3.2:5d}} | </div>{{#NAVCONTENT:Svar|Svar 3.2:5|Lösning a|Lösning 3.2:5a|Lösning b|Lösning 3.2:5b|Lösning c|Lösning 3.2:5c|Lösning d|Lösning 3.2:5d}} | ||
| - | === | + | ===Exercise 3.2:6=== |
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| - | + | Write the following numbers in polar form | |
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|a) | |a) | ||
Version vom 12:27, 4. Aug. 2008
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Exercise 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\, och \displaystyle \,w | b) | \displaystyle z+u\, och \displaystyle \,z-u |
| c) | \displaystyle 2z+w | d) | \displaystyle z-\overline{w}+u |
Svar
Laden...
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
Exercise 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.
Svar
Lösning
Exercise 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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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)} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
