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3.1 Übungen

Aus Online Mathematik Brückenkurs 2

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K (Robot: Automated text replacement (-Theory +Theorie))
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|width="50%"| <math>i^{\,20} + i^{\,11}</math>
|width="50%"| <math>i^{\,20} + i^{\,11}</math>
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</div>{{#NAVCONTENT:Answer|Answer 3.1:1|Solution a|Solution 3.1:1a|Solution b|Solution 3.1:1b|Solution c|Solution 3.1:1c|Solution d|Solution 3.1:1d|Solution e|Solution 3.1:1e|Solution f|Solution 3.1:1f}}
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</div>{{#NAVCONTENT:Antwort|Antwort 3.1:1|Solution a|Solution 3.1:1a|Solution b|Solution 3.1:1b|Solution c|Solution 3.1:1c|Solution d|Solution 3.1:1d|Solution e|Solution 3.1:1e|Solution f|Solution 3.1:1f}}
===Übung 3.1:2===
===Übung 3.1:2===
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|width="50%"| <math>\displaystyle\frac{5-\displaystyle\frac{1}{1+i}}{3i + \displaystyle\frac{i}{2-3i}}</math>
|width="50%"| <math>\displaystyle\frac{5-\displaystyle\frac{1}{1+i}}{3i + \displaystyle\frac{i}{2-3i}}</math>
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</div>{{#NAVCONTENT:Answer|Answer 3.1:2|Solution a|Solution 3.1:2a|Solution b|Solution 3.1:2b|Solution c|Solution 3.1:2c|Solution d|Solution 3.1:2d}}
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</div>{{#NAVCONTENT:Antwort|Antwort 3.1:2|Solution a|Solution 3.1:2a|Solution b|Solution 3.1:2b|Solution c|Solution 3.1:2c|Solution d|Solution 3.1:2d}}
===Übung 3.1:3===
===Übung 3.1:3===
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===Übung 3.1:4===
===Übung 3.1:4===
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|width="50%"| <math>(1+i)\overline{z}+iz = 3+5i</math>
|width="50%"| <math>(1+i)\overline{z}+iz = 3+5i</math>
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</div>{{#NAVCONTENT:Answer|Answer 3.1:4|Solution a|Solution 3.1:4a|Solution b|Solution 3.1:4b|Solution c|Solution 3.1:4c|Solution d|Solution 3.1:4d|Solution e|Solution 3.1:4e|Solution f|Solution 3.1:4f}}
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</div>{{#NAVCONTENT:Antwort|Antwort 3.1:4|Solution a|Solution 3.1:4a|Solution b|Solution 3.1:4b|Solution c|Solution 3.1:4c|Solution d|Solution 3.1:4d|Solution e|Solution 3.1:4e|Solution f|Solution 3.1:4f}}

Version vom 13:29, 10. Mär. 2009

       Theorie          Übungen      

Übung 3.1:1

Write in the form a+bi, where a and b are real numbers

a) (5−2i)+(3+5i) b) 3i−(2−i)
c) i(2+3i) d) (3−2i)(7+5i)
e) (1+i)(2−i)2 f) i20+i11

Antwort | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Übung 3.1:2

Write in the form a+bi, where a and b are real numbers,

a) 1+i3−2i b) 3i4−6i−1+i3+2i
c) 1+i3(2−i3)2 d) 5−11+i3i+i2−3i

Antwort | Solution a | Solution b | Solution c | Solution d

Übung 3.1:3

Determine the real number \displaystyle \,a\, such that the expression \displaystyle \ \displaystyle\frac{3+i}{2+ai}\ becomes purely imaginary (i.e. the real part equals zero).


Antwort | Solution

Übung 3.1:4

Solve the equations

a) \displaystyle z+3i=2z-2 b) \displaystyle (2-i) z= 3+2i
c) \displaystyle iz+2= 2z-3 d) \displaystyle (2+i) \overline{z} = 1+i
e) \displaystyle \displaystyle\frac{iz+1}{z+i} = 3+i f) \displaystyle (1+i)\overline{z}+iz = 3+5i

Antwort | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/3.1_%C3%9Cbungen“