3.1 Übungen
Aus Online Mathematik Brückenkurs 2
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Exercise 3.1:1
Write in the form \displaystyle \,a+bi\,, where \displaystyle \,a\, and \displaystyle \,b\, are real numbers
| a) | \displaystyle (5-2i)+(3+5i) | b) | \displaystyle 3i -(2-i) |
| c) | \displaystyle i(2+3i) | d) | \displaystyle (3-2i)(7+5i) |
| e) | \displaystyle (1+i)(2-i)^2 | f) | \displaystyle i^{\,20} + i^{\,11} |
Answer
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Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 3.1:2
Write in the form \displaystyle \,a+bi\,, where \displaystyle \,a\, and \displaystyle \,b\, are real numbers,
| a) | \displaystyle \displaystyle\frac{3-2i}{1+i} | b) | \displaystyle \displaystyle\frac{3i}{4-6i} - \displaystyle\frac{1+i}{3+2i} |
| c) | \displaystyle \displaystyle\frac{(2-i\sqrt{3}\,)^2}{1+i\sqrt{3}} | d) | \displaystyle \displaystyle\frac{5-\displaystyle\frac{1}{1+i}}{3i + \displaystyle\frac{i}{2-3i}} |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 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).
Answer
Solution
Exercise 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 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
