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3.1 Übungen

Aus Online Mathematik Brückenkurs 2

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K (Robot: Automated text replacement (-Svar +Answer))
K (Robot: Automated text replacement (-Lösning +Solution))
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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|Lösning 3.1:1a|Solution b|Lösning 3.1:1b|Solution c|Lösning 3.1:1c|Solution d|Lösning 3.1:1d|Solution e|Lösning 3.1:1e|Solution f|Lösning 3.1:1f}}
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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}}
===Exercise 3.1:2===
===Exercise 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|Lösning 3.1:2a|Solution b|Lösning 3.1:2b|Solution c|Lösning 3.1:2c|Solution d|Lösning 3.1:2d}}
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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}}
===Exercise 3.1:3===
===Exercise 3.1:3===
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</div>{{#NAVCONTENT:Answer|Answer 3.1:3|Solution|Lösning 3.1:3}}
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</div>{{#NAVCONTENT:Answer|Answer 3.1:3|Solution|Solution 3.1:3}}
===Exercise 3.1:4===
===Exercise 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|Lösning 3.1:4a|Solution b|Lösning 3.1:4b|Solution c|Lösning 3.1:4c|Solution d|Lösning 3.1:4d|Solution e|Lösning 3.1:4e|Solution f|Lösning 3.1:4f}}
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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}}

Version vom 07:30, 17. Sep. 2008

 
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Exercise 3.1:1

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

a) (52i)+(3+5i) b) 3i(2i)
c) i(2+3i) d) (32i)(7+5i)
e) (1+i)(2i)2 f) i20+i11

Exercise 3.1:2

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

a) 1+i32i b) 3i46i1+i3+2i
c) 1+i3(2i3)2 d) 511+i3i+i23i

Exercise 3.1:3

Determine the real number a such that the expression  3+i2+ai  becomes purely imaginary (i.e. the real part equals zero).


Exercise 3.1:4

Solve the equations

a) z+3i=2z2 b) (2i)z=3+2i
c) iz+2=2z3 d) (2+i)z=1+i
e) z+iiz+1=3+i f) (1+i)z+iz=3+5i